- 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 ℂ<sup>n</sup> 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
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- 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 ℂ<sup>n</sup> 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
