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The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds /
This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
|
| Colección: | London Mathematical Society student texts ;
31. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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|---|---|---|---|
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| 003 | OCoLC | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Rosenberg, Steven, |d 1951- |e author. | |
| 245 | 1 | 4 | |a The Laplacian on a Riemannian manifold : |b an introduction to analysis on manifolds / |c Steven Rosenberg, Boston University. |
| 264 | 1 | |a Cambridge, U.K. ; |a New York, NY, USA : |b Cambridge University Press, |c 1997. | |
| 264 | 4 | |c ©1997 | |
| 300 | |a 1 online resource (x, 174 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society student texts ; |v 31 | |
| 504 | |a Includes bibliographical references (pages 165-169) and index. | ||
| 505 | 0 | |a Introduction -- 1. The Laplacian on a Riemannian manifold -- 2. Elements of differential geometry -- 3. The construction of the Heat Kernel -- 4. The Heat equation approach to the Atiyah-singer index Theorem -- 5. Zeta functions of laplacians. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Riemannian manifolds. | |
| 650 | 0 | |a Laplacian operator. | |
| 650 | 6 | |a Variétés de Riemann. | |
| 650 | 6 | |a Laplacien. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Analytic. |2 bisacsh | |
| 650 | 7 | |a Laplacian operator. |2 fast |0 (OCoLC)fst00992600 | |
| 650 | 7 | |a Riemannian manifolds. |2 fast |0 (OCoLC)fst01097804 | |
| 650 | 7 | |a Laplace-Operator |2 gnd | |
| 650 | 7 | |a Riemannscher Raum |2 gnd | |
| 650 | 7 | |a Riemann, Variétés de. |2 ram | |
| 650 | 7 | |a Laplacien. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Rosenberg, Steven, 1951- |t Laplacian on a Riemannian manifold. |d Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997 |z 0521463009 |w (DLC) 96044262 |w (OCoLC)35637019 |
| 830 | 0 | |a London Mathematical Society student texts ; |v 31. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551355 |z Texto completo |
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