Metric Structures in Differential Geometry

Name: Metric Structures in Differential Geometry
Price: 97.47 USD
Availability: InStock
ISBN: 9780387204307

ISBN-10: 038720430X

ISBN-13: 9780387204307

Edition: 2004

Authors: Gerard Walschap

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Description:

In this work, G. Walschap provides an introduction to the theory of differentiable manifolds and fiber bundles.

Book details

List price: $99.99
Copyright year: 2004
Publisher: Springer New York
Publication date: 3/18/2004
Binding: Hardcover
Pages: 229
Size: 5.98" wide x 9.02" long x 0.75" tall
Weight: 2.530
Language: English



Preface



Differentiable Manifolds



Basic Definitions



Differentiable Maps



Tangent Vectors



The Derivative



The Inverse and Implicit Function Theorems



Submanifolds



Vector Fields



The Lie Bracket



Distributions and Frobenius Theorem



Multilinear Algebra and Tensors



Tensor Fields and Differential Forms



Integration on Chains



The Local Version of Stokes' Theorem



Orientation and the Global Version of Stokes' Theorem



Some Applications of Stokes' Theorem



Fiber Bundles



Basic Definitions and Examples



Principal and Associated Bundles



The Tangent Bundle of Sn



Cross-Sections of Bundles



Pullback and Normal Bundles



Fibrations and the Homotopy Lifting/Covering Properties



Grassmannians and Universal Bundles



Homotopy Groups and Bundles Over Spheres



Differentiable Approximations



Homotopy Groups



The Homotopy Sequence of a Fibration



Bundles Over Spheres



The Vector Bundles Over Low-Dimensional Spheres



Connections and Curvature



Connections on Vector Bundles



Covariant Derivatives



The Curvature Tensor of a Connection



Connections on Manifolds



Connections on Principal Bundles



Metric Structures



Euclidean Bundles and Riemannian Manifolds



Riemannian Connections



Curvature Quantifiers



Isometric Immersions



Riemannian Submersions



The Gauss Lemma



Length-Minimizing Properties of Geodesics



First and Second Variation of Arc-Length



Curvature and Topology



Actions of Compact Lie Groups



Characteristic Classes



The Weil Homomorphism



Pontrjagin Classes



The Euler Class



The Whitney Sum Formula for Pontrjagin and Euler Classes



Some Examples



The Unit Sphere Bundle and the Euler Class



The Generalized Gauss-Bonnet Theorem



Complex and Symplectic Vector Spaces



Chern Classes


Bibliography


Index