Old and New Aspects in Spectral Geometry

Old and New Aspects in Spectral Geometry by M.-E. Craioveanu, Mircea Puta, Themistocles RASSIAS.

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...

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Bibliographic Details
Main Authors: Craioveanu, M.-E (Author), Puta, Mircea (Author), RASSIAS, Themistocles (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2001.
Edition:1st ed. 2001.
Series:Mathematics and Its Applications ; 534
Springer eBook Collection.
Subjects:
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential geometry.
Applied mathematics.
Engineering mathematics.
Matrix theory.
Algebra.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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