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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 | ||
| ||
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 |
| Edizione | [1st ed.] |
| 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-9910825445803321 |
|
Yu Yanlin
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Index theory for symplectic paths with applications / Yiming Long
| Index theory for symplectic paths with applications / Yiming Long |
| Autore | Long, Yiming |
| Pubbl/distr/stampa | Basel ; Boston ; Berlin : Birkhäuser, c2002 |
| Descrizione fisica | xxiv, 380 p. : ill. ; 24 cm |
| Disciplina | 514.74 |
| Collana | Progress in mathematics ; 207 |
| Soggetto topico |
Index theory (Mathematics)
Hamiltonian systems Symplectic manifolds Iterative methods (Mathematics) |
| ISBN | 3764366478 |
| Classificazione |
AMS 37B30
AMS 34C25 AMS 58E05 AMS 70H03 AMS 70H05 AMS 70H12 LC QA614.92L66 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000573089707536 |
|
Long, Yiming
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| Basel ; Boston ; Berlin : Birkhäuser, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Index theory, coarse geometry, and topology of manifolds / John Roe
| Index theory, coarse geometry, and topology of manifolds / John Roe |
| Autore | Roe, John |
| Pubbl/distr/stampa | Providence (RI) : American Mathematical Society, c1996 |
| Descrizione fisica | ix, 100 p. ; 26 cm |
| Disciplina | 514.74 |
| Collana | CBMS Regional Conference Series in Mathematics |
| Soggetto non controllato |
Analisi globale
K - Teoria Analisi funzionale Topologia differenziale |
| ISBN | 0-8218-0413-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990001354620403321 |
|
Roe, John
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| Providence (RI) : American Mathematical Society, c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Integrability, self-duality and twistor theory / L. J. Mason, N. M. J. Woodhouse
| Integrability, self-duality and twistor theory / L. J. Mason, N. M. J. Woodhouse |
| Autore | Mason, L. J. |
| Pubbl/distr/stampa | Oxford : Clarendon Press, 1996 |
| Descrizione fisica | x, 364 p. : ill. ; 24 cm |
| Disciplina | 514.74 |
| Collana | London Mathematical Society monographs, New series |
| Soggetto non controllato |
Analisi globale
Analisi globale - Applicazioni alla fisica Twistor theory Equazioni in spazi di funzione |
| ISBN | 0-19-853498-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990001193330403321 |
|
Mason, L. J.
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| Oxford : Clarendon Press, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Integrable geodesic flows on two-dimensional surfaces / A. V. Bolsinov and A. T. Fomenko
| Integrable geodesic flows on two-dimensional surfaces / A. V. Bolsinov and A. T. Fomenko |
| Autore | Bolsinov, A. V. |
| Pubbl/distr/stampa | New York : Consultants Bureau, c2000 |
| Descrizione fisica | xiii, 322 p. : ill. ; 26 cm |
| Disciplina | 514.74 |
| Altri autori (Persone) | Fomenko, A. T. |
| Collana | Monographs in contemporary mathematics |
| Soggetto topico | Geodesic flows |
| ISBN | 0306110652 |
| Classificazione |
AMS 37E
AMS 37J AMS 70E AMS 70H LC QA614.82.B6513 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003685179707536 |
|
Bolsinov, A. V.
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| New York : Consultants Bureau, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Integrable hamiltonian hierarchies : Spectral and geometric methods / Vladimir Stefanov Gerdjikov...[et al.]
| Integrable hamiltonian hierarchies : Spectral and geometric methods / Vladimir Stefanov Gerdjikov...[et al.] |
| Autore | GERDJIKOV, Vladimir Stefanov |
| Pubbl/distr/stampa | Berlin [etc.] : Springer, copyr. 2008 |
| Descrizione fisica | XII, 643 p. ; 24 cm |
| Disciplina | 514.74 |
| Collana | Lecture notes in physics |
| Soggetto topico | Sistemi hamiltoniani |
| ISBN | 978-3-540-77053-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990003140950203316 |
|
GERDJIKOV, Vladimir Stefanov
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| Berlin [etc.] : Springer, copyr. 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
INTEGRABLE systems : The Verdier Memorial Conference Actes du Colloque International de Luminy / Editors Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach
| INTEGRABLE systems : The Verdier Memorial Conference Actes du Colloque International de Luminy / Editors Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach |
| Pubbl/distr/stampa | Boston [MA] : Birkhauser, c1993 |
| Descrizione fisica | xii, 366 p. ; 24 cm |
| Disciplina | 514.74 |
| Collana | Progress in mathematics |
| Soggetto non controllato |
Geometria differenziale - Congressi
Sistemi hamiltoniani - Congressi Matematici - 20. sec. - verdier j.-l. |
| ISBN | 0-8176-3653-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990001330580403321 |
| Boston [MA] : Birkhauser, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Integrable systems and quantum groups : lectures given at the 1. session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1993 / R. Donagi ... [et al.] ; editors M. Francaviglia, S. Greco
| Integrable systems and quantum groups : lectures given at the 1. session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1993 / R. Donagi ... [et al.] ; editors M. Francaviglia, S. Greco |
| Autore | Centro internazionale matematico estivo : <1993 |
| Pubbl/distr/stampa | Berlin [etc.] : Springer, c1996 |
| Descrizione fisica | VI, 488 p. ; 24 cm. |
| Disciplina | 514.74 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Geometria algebrica - Congressi
Fisica matematica - Congressi |
| ISBN | 3-540-60542-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNIBAS-000013861 |
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Centro internazionale matematico estivo : <1993
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| Berlin [etc.] : Springer, c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. della Basilicata | ||
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