Old and New Aspects in Spectral Geometry
It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoin...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Introduction to Riemannian Manifolds
- 2. Canonical Differential Operators Associated to a Riemannian Manifold
- 3. Spectral Properties of the Laplace-Beltrami Operator and Applications
- 4. Isospectral Closed Riemannian Manifolds
- 5. Spectral Properties of the Laplacians for the de Rham Complex
- 6. Applications to Geometry and Topology
- 7. An Introduction to Witten-Helffer-Sjöstrand Theory
- 8. Open Problems and Comments
- 1. Review of Matrix Algebra
- 2. Eigenvectors and Eigenvalues
- 3. Diagonalizable Matrices. Triangularizable Matrices. Jordan Canonical Form
- 4. Eigenvalues and Eigenvectors of Real Symmetric and Hermitian Matrices
- References