The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds

Couverture
Cambridge University Press, 9 janv. 1997 - 172 pages
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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Table des matières

III
8
IV
8
V
8
VI
8
VII
10
IX
14
X
17
XI
22
XXIII
90
XXIV
92
XXV
96
XXVI
101
XXVII
108
XXVIII
111
XXIX
112
XXX
116

XIII
27
XIV
33
XV
35
XVI
39
XVII
46
XVIII
52
XIX
63
XX
67
XXI
79
XXII
85
XXXI
128
XXXIII
134
XXXIV
139
XXXV
144
XXXVI
153
XXXVIII
154
XXXIX
163
XL
167
XLI
172
Droits d'auteur

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Expressions et termes fréquents

Fréquemment cités

Page 168 - J. Cheeger and S.-T. Yau, A lower bound for the heat kernel, Commun. Pure Appl.
Page 169 - Automorphe Formen und der Satz von Riemann-Roch, Symposium International de Topologia Algebraica, UNESCO, 1958, pp.
Page 169 - S. Kudla and J. Millson, Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math.

Informations bibliographiques