The Laplacian on a Riemannian manifold
- Utgiven: 1997
- ISBN: 9780521468312
- Sidor: 188 st
- Förlag: Cambridge University Press
- Format: Häftad
- Språk: Engelska
Om boken
This text on analysis on 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 author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also treats zeta functions for Laplacians and analytic torsion, and lays out the recently uncovered relation between index theory and analytic torsion. The text is aimed at students who have had a first course in differentiable manifolds, and the author develops the Riemannian geometry used from the beginning. There are over 100 exercises with hints.
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Mer om The Laplacian on a Riemannian manifold (1997)
1997 släpptes boken The Laplacian on a Riemannian manifold skriven av Steven Rosenberg. Den är skriven på engelska och består av 188 sidor. Förlaget bakom boken är Cambridge University Press.
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Referera till The Laplacian on a Riemannian manifold
Harvard
Rosenberg, S. (1997). The Laplacian on a Riemannian manifold. Cambridge University Press.
Oxford
Rosenberg, Steven, The Laplacian on a Riemannian manifold (Cambridge University Press, 1997).
APA
Rosenberg, S. (1997). The Laplacian on a Riemannian manifold. Cambridge University Press.
Vancouver
Rosenberg S. The Laplacian on a Riemannian manifold. Cambridge University Press; 1997.
