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The Laplacian on a Riemanni...

The Laplacian on a Riemannian manifold [an introduction to analysis on manifolds

Rosenberg, Steven (1951-)

Cambridge University Press 1997

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds

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monografia Rebiun28714529 https://catalogo.rebiun.org/rebiun/record/Rebiun28714529 m o d | cr -n--------- 960920s1997 enk ob 001 0 eng d 96044262 1-316-08717-4 0-511-94467-5 1-107-36206-7 0-511-62378-X 1-107-36697-6 1-299-40908-3 1-107-36451-5 UPVA 998450068803706 UAM 991008076773804211 CBUC 991010752356606709 MiAaPQ MiAaPQ MiAaPQ eng 515.373 516.3/73 516.373 Rosenberg, Steven 1951-) The Laplacian on a Riemannian manifold electronic resource] :] an introduction to analysis on manifolds Steven Rosenberg Cambridge, U.K. New York Cambridge University Press 1997 Cambridge, U.K. New York Cambridge, U.K. New York Cambridge University Press 1 online resource (186 p.) 1 online resource (186 p.) Text txt computer c online resource cr London Mathematical Society student texts 31 Description based upon print version of record Includes bibliographical references and index Cover; Title; Copyright; Contents; Introduction; 1 The Laplacian on aRiemannian Manifold; 1.1 Basic Examples; 1.1.1 The Laplacian on S1 and R; 1.1.2 Heat Flow on S1 and R; 1.2 The Laplacian on a Riemannian Manifold; 1.2.1 Riemannian Metrics; 1.2.2 L2 Spaces of Functions and Forms; 1.2.3 The Laplacian on Functions; 1.3 Hodge Theory for Functions and Forms; 1.3.1 Analytic Preliminaries; 1.3.2 The Heat Equation Proof of the Hodge Theorem forFunctions; 1.3.3 The Hodge Theorem for Differential Forms; 1.3.4 Regularity Results; 1.4 De Rham Cohomology; 1.5 The Kernel of the Laplacian on Forms 2 Elements of DifferentialGeometry2.1 Curvature; 2.2 The Levi-Civita Connection and BochnerFormula; 2.2.1 The Levi-Civita Connection; 2.2.2 Weitzenböck Formulas and Garding's Inequality; 2.3 Geodesies; 2.4. The Laplacian in Exponential Coordinates; 3 The Construction of theHeat Kernel; 3.1 Preliminary Results for the Heat Kernel; 3.2 Construction of the Heat Kernel; 3.2.1 Construction of the Parametrix; 3.2.2 The Heat Kernel for Functions; 3.3. The Asymptotics of the Heat Kernel; 3.4 Positivity of the Heat Kernel; 4 The Heat EquationApproach to theAtiyah-Singer IndexTheorem 4.1 The Chern-Gauss-Bonnet Theorem4.1.1 The Heat Equation Approach; 4.1.2 Proof of the Chern-Gauss-Bonnet Theorem; 4.2 The Hirzebruch Signature Theorem and the Atiyah-Singer Index Theorem; 4.2.1 A Survey of Characteristic Forms; 4.2.2 The Hirzebruch Signature Theorem; 4.2.3 The Atiyah-Singer Index Theorem; 5 Zeta Functions ofLaplacians; 5.1 The Zeta Function of a Laplacian; 5.2 Isospectral Manifolds; 5.3 Reidemeister Torsion and Analytic Torsion; 5.3.1 Reidemeister Torsion; 5.3.2 Analytic Torsion; 5.3.3 The Families Index Theorem and Analytic Torsion; Bibliography; Index This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds English Riemannian manifolds Laplacian operator Electronic books 0-521-46300-9 0-521-46831-0 London Mathematical Society student texts 31

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monografia Rebiun28714529 https://catalogo.rebiun.org/rebiun/record/Rebiun28714529 m o d | cr -n--------- 960920s1997 enk ob 001 0 eng d 96044262 1-316-08717-4 0-511-94467-5 1-107-36206-7 0-511-62378-X 1-107-36697-6 1-299-40908-3 1-107-36451-5 UPVA 998450068803706 UAM 991008076773804211 CBUC 991010752356606709 MiAaPQ MiAaPQ MiAaPQ eng 515.373 516.3/73 516.373 Rosenberg, Steven 1951-) The Laplacian on a Riemannian manifold electronic resource] :] an introduction to analysis on manifolds Steven Rosenberg Cambridge, U.K. New York Cambridge University Press 1997 Cambridge, U.K. New York Cambridge, U.K. New York Cambridge University Press 1 online resource (186 p.) 1 online resource (186 p.) Text txt computer c online resource cr London Mathematical Society student texts 31 Description based upon print version of record Includes bibliographical references and index Cover; Title; Copyright; Contents; Introduction; 1 The Laplacian on aRiemannian Manifold; 1.1 Basic Examples; 1.1.1 The Laplacian on S1 and R; 1.1.2 Heat Flow on S1 and R; 1.2 The Laplacian on a Riemannian Manifold; 1.2.1 Riemannian Metrics; 1.2.2 L2 Spaces of Functions and Forms; 1.2.3 The Laplacian on Functions; 1.3 Hodge Theory for Functions and Forms; 1.3.1 Analytic Preliminaries; 1.3.2 The Heat Equation Proof of the Hodge Theorem forFunctions; 1.3.3 The Hodge Theorem for Differential Forms; 1.3.4 Regularity Results; 1.4 De Rham Cohomology; 1.5 The Kernel of the Laplacian on Forms 2 Elements of DifferentialGeometry2.1 Curvature; 2.2 The Levi-Civita Connection and BochnerFormula; 2.2.1 The Levi-Civita Connection; 2.2.2 Weitzenböck Formulas and Garding's Inequality; 2.3 Geodesies; 2.4. The Laplacian in Exponential Coordinates; 3 The Construction of theHeat Kernel; 3.1 Preliminary Results for the Heat Kernel; 3.2 Construction of the Heat Kernel; 3.2.1 Construction of the Parametrix; 3.2.2 The Heat Kernel for Functions; 3.3. The Asymptotics of the Heat Kernel; 3.4 Positivity of the Heat Kernel; 4 The Heat EquationApproach to theAtiyah-Singer IndexTheorem 4.1 The Chern-Gauss-Bonnet Theorem4.1.1 The Heat Equation Approach; 4.1.2 Proof of the Chern-Gauss-Bonnet Theorem; 4.2 The Hirzebruch Signature Theorem and the Atiyah-Singer Index Theorem; 4.2.1 A Survey of Characteristic Forms; 4.2.2 The Hirzebruch Signature Theorem; 4.2.3 The Atiyah-Singer Index Theorem; 5 Zeta Functions ofLaplacians; 5.1 The Zeta Function of a Laplacian; 5.2 Isospectral Manifolds; 5.3 Reidemeister Torsion and Analytic Torsion; 5.3.1 Reidemeister Torsion; 5.3.2 Analytic Torsion; 5.3.3 The Families Index Theorem and Analytic Torsion; Bibliography; Index This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds English Riemannian manifolds Laplacian operator Electronic books 0-521-46300-9 0-521-46831-0 London Mathematical Society student texts 31