Differential geometry of manifolds / Stephen Lovett

By:

Lovett, Stephen [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Textbooks in Mathematics SerPublisher: Milton : CRC Press LLC, 2019Edition: Second editionDescription: 1 Online-Ressource (451 pages)ISBN:

9780429059292
9780429607820
9780429602306

Subject(s):

Additional physical formats: 9780367180461 | Erscheint auch als: Differential geometry of manifolds. Druck-Ausgabe Second edition. Boca Raton : CRC Press, 2020. xiii, 436 SeitenRVK: RVK: SK 370LOC classification:

QA649

Online resources:

Zugang im Netz des KIT

Summary: 3.2 Differentiable Maps between Manifolds -- 3.3 Tangent Spaces -- 3.4 The Differential of a Differentiable Map -- 3.5 Manifolds with Boundaries -- 3.6 Immersions, Submersions, and Submanifolds -- 3.7 Orientability -- 4: Multilinear Algebra -- 4.1 Hom Space and Dual -- 4.2 Bilinear Forms and Inner Products -- 4.3 Adjoint, Self-Adjoint, and Automorphisms -- 4.4 Tensor Product -- 4.5 Components of Tensors over V -- 4.6 Symmetric and Alternating Products -- 4.7 Algebra over a Field -- 5: Analysis on Manifolds -- 5.1 Vector Bundles on Manifolds -- 5.2 Vector and Tensor Fields on ManifoldsSummary: 5.3 Lie Bracket and Lie Derivative -- 5.4 Differential Forms -- 5.5 Pull-Backs of Covariant Tensor Fields -- 5.6 Lie Derivative of Tensor Fields -- 5.7 Integration on Manifolds -- Definition -- 5.8 Integration on Manifolds -- Applications -- 5.9 Stokes' Theorem -- 6: Introduction to Riemannian Geometry -- 6.1 Riemannian Metrics -- 6.2 Connections and Covariant Differentiation -- 6.3 Vector Fields along Curves -- Geodesics -- 6.4 Curvature Tensor -- 6.5 Ricci Curvature and Einstein Tensor -- 7: Applications of Manifolds to Physics -- 7.1 Hamiltonian Mechanics -- 7.2 Special RelativitySummary: Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Acknowledgments -- 1: Analysis of Multivariable Functions -- 1.1 Functions from ℝn to ℝm -- 1.2 Continuity, Limits, and Differentiability -- 1.3 Differentiation Rules -- Functions of Class Cr -- 1.4 Inverse and Implicit Function Theorems -- 2: Variable Frames -- 2.1 Frames Associated to Coordinate Systems -- 2.2 Frames Associated to Trajectories -- 2.3 Variable Frames and Matrix Functions -- 3: Differentiable Manifolds -- 3.1 Definitions and ExamplesSummary: Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a both streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics. The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, string theory. The Second Edition of this successful textbook offers several notable points of revision. New to the Second Edition: New problems have been added and the level of challenge has been changed to the exercises Each section corresponds to a 60-minute lecture period, making it more user-friendly for lecturers Includes new sections which provide more comprehensive coverage of topics Features a new chapter on Multilinear AlgebraSummary: Pseudo-Riemannian Manifolds -- 7.3 Electromagnetism -- 7.4 Geometric Concepts in String Theory -- 7.5 Brief Introduction to General Relativity -- A: Point Set Topology -- A.1 Metric Spaces -- A.2 Topological Spaces -- B: Calculus of Variations -- B.1 Formulation of Several Problems -- B.2 Euler-Lagrange Equation -- B.3 Several Dependent Variables -- B.4 Isoperimetric Problems and Lagrange Multipliers -- C: Further Topics in Multilinear Algebra -- C.1 Binet-Cauchy and k-Volume of Parallelepipeds -- C.2 Volume Form Revisited -- C.3 Hodge Star Operator -- Bibliography -- IndexPPN: PPN: 1755160070Package identifier: Produktsigel: BSZ-4-NLEBK-KAUB | ZDB-4-NLEBK

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