Differential Geometric Structures
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Read More ↓Title Statements
- Full title :Differential Geometric Structures.
Summary
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Read More ↓Edition Statements
- Publication Date:2015.
Publication Statements
- Publisher(s):Dover Publications
- Place of Publication:Newburyport
- Language:eng
- Publication Date:2015.
The Physical Object
- Description:1 online resource (651 pages)
Edition Identifiers
- ISBN:9780486151915, 0486151913
- oclc:ocn908671234
- LC Classification:QA641 .P616 2015
- Dewey Decimal:516.3/6
Table of Contents
Cover; Title Page; Copyright Page; Dedication; Contents; Preface; Chapter 1: An Introduction to Fiber Bundles; The Definition of a Fiber Bundle; Vector Bundles; The Vertical Bundle; Operations on Vector Bundles; Principal and Associated Bundles; Sections of Fiber Bundles; Chapter 2: Connection Theory for Vector Bundles; Parallelism Structures in Vector Bundles; Holonomy in Vector Bundles; Connections on Vector Bundles; The Curvature Tensor; Covariant Derivative Operators; The Structure Equation; The Space of Connections on a Vector Bundle; Characteristic Classes.
The Tangent Bundle: Linear ConnectionsThe Tangent Bundle: Affine Connections; Affine Transformations; Chapter 3: Riemannian Vector Bundles; Riemannian Metrics; Riemannian Connections; The Levi-Civita Connection; The Metric Structure of a Riemannian Manifold; The Gauss-Bonnet Theorem; Chapter 4: Harmonic Theory; The Basic Differential Operators; Green's Theorem and Some Applications; Weitzenböck's Formula for the Laplacian; Chern's Formula for the Laplacian; Chapter 5: Geometric Vector Fields on Riemannian Manifolds; Harmonic Fields; Killing Fields; Conformal Fields; Affine Fields.
Projective FieldsChapter 6: Lie Groups;…
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