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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
|
| Schriftenreihe: | London Mathematical Society student texts ;
31. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (x, 174 pages) |
| Bibliographie: | Includes bibliographical references (pages 165-169) and index. |
| ISBN: | 9781107362062 1107362067 9780511623783 051162378X 9780511961540 0511961545 |
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| 245 | 1 | 4 | |a The Laplacian on a Riemannian manifold : |b an introduction to analysis on manifolds / |c Steven Rosenberg, Boston University. |
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| 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. | ||
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| contents | 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. |
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| discipline | Mathematik |
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| spelling | Rosenberg, Steven, 1951- author. https://id.oclc.org/worldcat/entity/E39PCjCtqCgvWxXtdpJxY6MQMP http://id.loc.gov/authorities/names/n96092183 The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / Steven Rosenberg, Boston University. Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997. ©1997 1 online resource (x, 174 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 31 Includes bibliographical references (pages 165-169) and index. 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. Print version record. 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. Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Laplacian operator. http://id.loc.gov/authorities/subjects/sh85074667 Variétés de Riemann. Laplacien. MATHEMATICS Geometry Analytic. bisacsh Laplacian operator fast Riemannian manifolds fast Laplace-Operator gnd http://d-nb.info/gnd/4166772-4 Riemannscher Raum gnd Riemann, Variétés de. ram Laplacien. ram has work: The Laplacian on a Riemannian manifold (Text) https://id.oclc.org/worldcat/entity/E39PCGc8Y7tvWyXBGPCQJ3vQ4m https://id.oclc.org/worldcat/ontology/hasWork Print version: Rosenberg, Steven, 1951- Laplacian on a Riemannian manifold. Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997 0521463009 (DLC) 96044262 (OCoLC)35637019 London Mathematical Society student texts ; 31. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551355 Volltext |
| spellingShingle | Rosenberg, Steven, 1951- The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / London Mathematical Society student texts ; 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. Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Laplacian operator. http://id.loc.gov/authorities/subjects/sh85074667 Variétés de Riemann. Laplacien. MATHEMATICS Geometry Analytic. bisacsh Laplacian operator fast Riemannian manifolds fast Laplace-Operator gnd http://d-nb.info/gnd/4166772-4 Riemannscher Raum gnd Riemann, Variétés de. ram Laplacien. ram |
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| title | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / |
| title_auth | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / |
| title_exact_search | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / |
| title_full | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / Steven Rosenberg, Boston University. |
| title_fullStr | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / Steven Rosenberg, Boston University. |
| title_full_unstemmed | The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds / Steven Rosenberg, Boston University. |
| title_short | The Laplacian on a Riemannian manifold : |
| title_sort | laplacian on a riemannian manifold an introduction to analysis on manifolds |
| title_sub | an introduction to analysis on manifolds / |
| topic | Riemannian manifolds. http://id.loc.gov/authorities/subjects/sh85114045 Laplacian operator. http://id.loc.gov/authorities/subjects/sh85074667 Variétés de Riemann. Laplacien. MATHEMATICS Geometry Analytic. bisacsh Laplacian operator fast Riemannian manifolds fast Laplace-Operator gnd http://d-nb.info/gnd/4166772-4 Riemannscher Raum gnd Riemann, Variétés de. ram Laplacien. ram |
| topic_facet | Riemannian manifolds. Laplacian operator. Variétés de Riemann. Laplacien. MATHEMATICS Geometry Analytic. Laplacian operator Riemannian manifolds Laplace-Operator Riemannscher Raum Riemann, Variétés de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551355 |
| work_keys_str_mv | AT rosenbergsteven thelaplacianonariemannianmanifoldanintroductiontoanalysisonmanifolds AT rosenbergsteven laplacianonariemannianmanifoldanintroductiontoanalysisonmanifolds |