- Title Pages
- Preface
-
1 Smooth manifolds -
2 Matrices and Lie groups -
3 Introduction to vector bundles -
4 Algebra of vector bundles -
5 Maps and vector bundles -
6 Vector bundles with ℂn as fiber -
7 Metrics on vector bundles -
8 Geodesics -
9 Properties of geodesics -
10 Principal bundles -
11 Covariant derivatives and connections -
12 Covariant derivatives, connections and curvature -
13 Flat connections and holonomy -
14 Curvature polynomials and characteristic classes -
15 Covariant derivatives and metrics -
16 The Riemann curvature tensor -
17 Complex manifolds -
18 Holomorphic submanifolds, holomorphic sections and curvature -
19 The Hodge star - List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index
The Hodge star
The Hodge star
- Chapter:
- (p.282) 19 The Hodge star
- Source:
- Differential Geometry
- Author(s):
Clifford Henry Taubes
- Publisher:
- Oxford University Press
This chapter first provides a definition of the Hodge star. It then discusses representatives of De Rham cohomology; presents the Hodge theorem; and explains the notion of self-duality.
Keywords: Hodge theorem, De Rham cohomology, self-duality
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
- Title Pages
- Preface
-
1 Smooth manifolds -
2 Matrices and Lie groups -
3 Introduction to vector bundles -
4 Algebra of vector bundles -
5 Maps and vector bundles -
6 Vector bundles with ℂn as fiber -
7 Metrics on vector bundles -
8 Geodesics -
9 Properties of geodesics -
10 Principal bundles -
11 Covariant derivatives and connections -
12 Covariant derivatives, connections and curvature -
13 Flat connections and holonomy -
14 Curvature polynomials and characteristic classes -
15 Covariant derivatives and metrics -
16 The Riemann curvature tensor -
17 Complex manifolds -
18 Holomorphic submanifolds, holomorphic sections and curvature -
19 The Hodge star - List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index
