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csikos b differential geometry 2019

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Textbook in PDF format Preliminaries Categories and Functors Linear Algebra Linear Spaces and Linear Maps Determinant of Matrices and Linear Endomorphisms Orientation of a Linear Space Tensor Product Exterior Powers Euclidean Linear Spaces Hodge Star Operator Geometry Affine Geometry Euclidean Spaces Topology Separation and Countability Axioms Compactness Fundamental Group and Covering Spaces Multivariable Calculus Measure and Integration Ordinary Differential Equations Curves in En The Notion of a Curve The Length of a Curve Crofton's Formula The Osculating k-planes Frenet Frames and Curvatures Limits of Some Geometrical Quantities Osculating Spheres Plane Curves Evolute, Involute, Parallel Curves The Rotation Number Theorem Convex Curves The Four Vertex Theorem Curves in R3 Orthogonal Projections onto Planes Spanned by Frenet Vectors Fenchel's Theorem The Fáry-Milnor Theorem Hypersurfaces in Rn General Theory Definition of a Parameterized Hypersurface Curvature of Curves on a Hypersurface The Weingarten Map and the Fundamental Forms Umbilical Points The Fundamental Equations of Hypersurface Theory Surface Volume Surfaces in R3 Surfaces of Revolution Lines of Curvature, Triply Orthogonal Systems Ruled and Developable Surfaces Asymptotic Curves on Negatively Curved Surfaces Surfaces of Constant Negative Curvature Minimal Surfaces Manifolds Topological and Differentiable Manifolds Basic Definitions Configuration Spaces Submanifolds of Rn Remarks on the Classification of Manifolds The Tangent Bundle The Tangent Bundle The Derivative of a Smooth Map The Lie Algebra of Vector Fields The Lie Algebra of Lie Groups Subspace Distributions and the Frobenius Theorem Tensor Bundles and Tensor Fields The Lie Derivative Differential Forms Interior Product by a Vector Field Exterior Differentiation De Rham Cohomology Integration of Differential Forms Integration on Chains Integration on Regular Domains Integration on Riemannian Manifolds Differentiation of Vector Fields Curvature Decomposition of Algebraic Curvature Tensors Conformal Invariance of the Weyl Tensor Geodesics Applications to Hypersurface Theory Geodesic Curves on Hypersurfaces Clairaut's Theorem Moving Orthonormal Frames Along a Hypersurface Relation to Earlier Formulae for Parameterized Hypersurfaces The Gauss–Bonnet Formula Steiner's Formula Minkowski's Formula Rigidity of Convex Surfaces Bibliography Index

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Csikos B. Differential Geometry 2019.pdf 7.8 MB

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csikos b differential geometry 2019