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The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu
| The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu |
| Autore | Yu Yanlin |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 514.74 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Atiyah-Singer index theorem
Heat equation |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-95164-1
9786611951641 981-281-010-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation
2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| Record Nr. | UNINA-9910454372203321 |
Yu Yanlin
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu
| The index theorem and the heat equation method [[electronic resource] /] / Yanlin Yu |
| Autore | Yu Yanlin |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 514.74 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Atiyah-Singer index theorem
Heat equation |
| ISBN |
1-281-95164-1
9786611951641 981-281-010-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation
2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX |
| Record Nr. | UNINA-9910782394003321 |
|
Yu Yanlin
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||