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Lectures on Differential Geometry

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Differentiable Manifolds
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Topics in Differential Geometry
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Geological Priors and Inversion
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A solution of the non‐uniqueness problem of the Dirac Hamiltonian and energy operators
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Intrinsic Differential Geometry with Geometric Calculus
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Shape Matching by Variational Computation of Geodesics on a Manifold
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Symmetry and Perturbation Theory in Non-linear Dynamics
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Non-linear Dynamics, Symmetry and Perturbation Theory in
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Background on Differential Geometry
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Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian
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Introduction
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Manifolds
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Skin Friction from Surface Pressure Visualizations
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Differential Constructs
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An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity
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Curvature
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G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion
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Pseudo-complex Differential Geometry
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Vector Fields and Ordinary Differential Equations
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Foundations of Mathematics and Physics One Century After Hilbert
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The Dressing Field Method of Gauge Symmetry Reduction, a Review with Examples
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The Dual Approach to Smooth Defects
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Automatic Flight Control Systems
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Differentiable Manifold
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Manifolds
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Riemannian Geometry
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Flatness Characterization: Two Approaches
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Nonlinear Dynamics, Symmetry and Perturbation Theory in
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Ellipsoid-of-Revolution to Tangential Plane
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Ellipsoid-of-Revolution to Sphere and from Sphere to Plane
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Differential Forms
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Introduction
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Extension of Design Space: Topology Optimization on Two-Dimensional Manifolds for Wave Optics
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Lie Derivatives, Killing Fields and Hypersurfaces
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Differential Forms and Their Integrals
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Geometry of systems of differential equations. VII. Applications and examples
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Holomorphic manifolds on locally convex spaces
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Surfaces Associated with First-Order ODEs
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Ruled surfaces of Weingarten type in Minkowski 3-space
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Minimal hypersurfaces in conformally flat spaces
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Negative Curvature Constricts the Fundamental Gap of Convex Domains
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On Solutions for Strongly Coupled Critical Elliptic Systems on Compact Riemannian Manifolds
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Fiber bundle topology optimization of hierarchical microtextures for wetting behavior in Cassie-Baxter mode
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Moduli of Vortices and Grassmann Manifolds
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Existence and Rigidity of Quantum Isometry Groups for Compact Metric Spaces
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Derivatives of Siegel modular forms and modular connections
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A Geometric Field Theory of Dislocation Mechanics
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Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications
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Variational Sequences in Mechanics on Grassmann Fibrations
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Left Lie reduction for curves in homogeneous spaces
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The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula
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The Hodge–de Rham decomposition theorem and an application to a partial differential equation
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Incompatible deformation field and Riemann curvature tensor
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Barbilian’s metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics
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Existence of isometric immersions into nilpotent Lie groups
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Geometric Proof of Exact Quantization Rules in One Dimensional Quantum Mechanics
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Finsler Streamline Tracking with Single Tensor Orientation Distribution Function for High Angular Resolution Diffusion Imaging
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Polyakov Soldering and Second-Order Frames: The Role of the Cartan Connection
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A Lie group formulation of Kane’s equations for multibody systems
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The d’Alembert–Lagrange equation exploited on a Riemannian manifold
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On One Family of Minimal Tori in ℝ3 with Planar Embedded Ends
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Eigenvalue comparison theorems on Finsler manifolds
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Kinematic formulas of total mean curvatures for hypersurfaces
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Equivalent properties for CD inequalities on graphs with unbounded Laplacians
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A Gauss-Bonnet-Chern theorem for complex Finsler manifolds
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Differential operators for Siegel-Jacobi forms
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A ubiquitous knowledgeable data representation model (UKRM) for three-dimensional geographic information systems (3D GIS)
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A manifold approach to generating iso-scallop trajectories in three-axis machining
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Algorithmic challenges in structure-based drug design and NMR structural biology
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Calabi-Yau metrics on compact Kähler manifolds with some divisors deleted
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Simplifying a shape manifold as linear manifold for shape analysis
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LLE-based classification algorithm for MMW radar target recognition
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Schur theorem for the Ricci curvature of any weakly Landsberg Finsler metric
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Global Differential Geometry of Curves in Three-Dimensional Heisenberg Group and CR Sphere
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Sharp Hardy Inequalities via Riemannian Submanifolds
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On Gauge Transforms of Autonomous Ordinary Differential Equations
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Local invariants of divergence-free webs
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Finsler geodesics, periodic Reeb orbits, and open books
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Non-linear Dynamics, Symmetry and Perturbation Theory in
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Lyapunov functions and isolating blocks
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Equivalence problems for first order Lagrangians on the line
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The b-spectral sequence, Lagrangian formalism, and conservation laws. II. The nonlinear theory
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Mean value properties of solutions to parabolic equations with variable coefficients
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Geometrical formulation of equilibrium phenomenological thermodynamics
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The CR problem and Hurwitz pairs applied to field theory and solid state physics
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Higher order conservation laws and a higher order Noether's theorem
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REMOVED: REFERENCES
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References
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Reactive navigation of wheeled robots for border patrolling
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Safe navigation to a target in unknown cluttered static environments based on border patrolling algorithms
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Global aspects of Finsler geometry
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Admissible vectors for mock metaplectic representations
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Multiplication operators on the Bergman space via analytic continuation
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The Poincaré–Lyapounov–Nekhoroshev theorem for involutory systems of vector fields
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Geometric obstruction of black holes
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A method for guidance and control of an autonomous vehicle in problems of border patrolling and obstacle avoidance
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Orbital decompositions and integrable pseudosymmetries of control systems
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A generalized geometric spectral conjugate gradient algorithm for finding zero of a monotone tangent vector field on a constant curvature Hadamard manifold
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Shape synchronization control for three-dimensional chaotic systems
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Asymptotic shape synchronization in three-dimensional chaotic systems and its application in color image encryption
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Topology optimization on two-dimensional manifolds
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Spherical harmonics-based pseudo-spectral method for quantitative analysis of symmetry breaking in wrinkling of shells with soft cores
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Event-triggered impulse control on reaction–diffusion Gilpin–Ayala competition model with multiple stationary solutions
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Nonlinear dimensionality reduction of gene expression data for visualization and clustering analysis of cancer tissue samples
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Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues
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On the Gauss–Bonnet–Chern formula for real Finsler vector bundles
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3-dimensional left-invariant sub-Lorentzian contact structures
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On dynamics of molecular media
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Calculation of the Behavior Utility of a Network System: Conception and Principle
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Efficient hyper reduced-order model (HROM) for parametric studies of the 3D thermo-elasto-plastic calculation
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Geometrical origin of the -product in the Fedosov formalism
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A gauge-theoretic description of μ -prolongations, and μ -symmetries of differential equations
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Surfaces specified by integrable systems of partial differential equations determined by structure equations and Lax pair
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Covariant derivatives for Ehresmann connections
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The fundamental theorem of Legendrian submanifolds in the Heisenberg group
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The Gauss formulas for Laplacians on submanifolds
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The integrability conditions and Euler-Poincaré characteristic for hypersurfaces in Heisenberg groups
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A differential geometry approach to analysis of thermal forming
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Geometry of slow–fast Hamiltonian systems and Painlevé equations
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Approximation order from stability for nonlinear subdivision schemes
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Locating omega-limit sets using height functions
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Global Yamabe flow on asymptotically flat manifolds
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The Kustaanheimo–Stiefel map, the Hopf fibration and the square root map on R3 and R4
inferred← citeshttps://doi.org/10.1016/j.jmaa.2013.06.070openalex-snapshot
Hardy and Rellich type inequalities on complete manifolds
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Exterior differential expression of the (1 + 1)-dimensional nonlinear evolution equation with Lax integrability
inferred← citeshttps://doi.org/10.1016/j.jmaa.2017.10.036openalex-snapshot
Improved Hardy and Rellich inequalities on nonreversible Finsler manifolds
inferred← citeshttps://doi.org/10.1016/j.jmaa.2021.124998openalex-snapshot
Uniqueness of exterior differentiation on locally finite graphs
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Reading mathematics for understanding—From novice to expert
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Effect of forward kinematics on the motion-trajectory oscillations and inertia forces
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Anchor graph based connectivity peaks clustering
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On asymptotic rigidity and continuity problems in nonlinear elasticity on manifolds and hypersurfaces
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Affine n-dimensional Statics, affine screws and Grassmann algebra
inferred← citeshttps://doi.org/10.1016/j.mechrescom.2021.103696openalex-snapshot
On Nye’s lattice curvature tensor
inferred← citeshttps://doi.org/10.1016/j.molliq.2022.121167openalex-snapshot
Geometric model of real gases described by the Redlich-Kwong-Soave equation of state
inferred← citeshttps://doi.org/10.1016/j.na.2021.112554openalex-snapshot
On the equation DutHDu=G
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Revived transformation-based transfer learning safety control: A geometric interpretation
inferred← citeshttps://doi.org/10.1016/j.nonrwa.2007.08.023openalex-snapshot
On Finsler manifolds with the Chern–Rund connection whose projectivised tangent bundle has the Sasaki type metric
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Sectional curvature bounds in gravity: regularisation of the Schwarzschild singularity
inferred← citeshttps://doi.org/10.1016/j.physa.2012.06.035openalex-snapshot
An intermediate distribution between Gaussian and Cauchy distributions
inferred← citeshttps://doi.org/10.1016/j.physd.2009.05.005openalex-snapshot
An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems
inferred← citeshttps://doi.org/10.1016/j.physd.2024.134162openalex-snapshot
Drive–response asymptotic shape synchronization for a class of two-dimensional chaotic systems and its application in image encryption
inferred← citeshttps://doi.org/10.1016/j.physe.2015.10.011openalex-snapshot
Curvature-induced bound states and coherent electron transport on the surface of a truncated cone
inferred← citeshttps://doi.org/10.1016/j.physleta.2009.11.042openalex-snapshot
Integrable systems of partial differential equations determined by structure equations and Lax pair
inferred← citeshttps://doi.org/10.1016/j.sigpro.2015.08.020openalex-snapshot
Active contours driven by divergence of gradient vector flow
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High probability analysis of the condition number of sparse polynomial systems
inferred← citeshttps://doi.org/10.1016/j.ymssp.2020.106690openalex-snapshot
Automatic detection of feather defects using Lie group and fuzzy Fisher criterion for shuttlecock production
inferred← citeshttps://doi.org/10.1016/s0020-7683(97)00087-5openalex-snapshot
Strain measures, integrability condition and frame indifference in the theory of oriented media
inferred← citeshttps://doi.org/10.1016/s0020-7683(99)00067-0openalex-snapshot
Tubes in tubes: catheter navigation in blood vessels and its applications
inferred← citeshttps://doi.org/10.1016/s0034-4877(16)30060-xopenalex-snapshot
Finsler Connection for General Lagrangian Systems
inferred← citeshttps://doi.org/10.1016/s0034-4877(23)00068-xopenalex-snapshot
A metrical approach to finsler geometry
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References
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Homogeneous domains in the space of complex structures
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A new lower bound for the integral of the (n − 2)nd mean curvature over the boundary of a compact domain in Rn
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Dido's Problem with a Fixed Center of Mass
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Finsler Geometry on Complex Vector Bundles
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