Lectures on Kahler Geometry
Andrei Moroianu - Collection London Mathematical Society Student Texts
Résumé
Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi-Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
- The first graduate-level text on Kähler geometry, providing a concise introduction for both mathematicians and physicists with a basic knowledge of calculus in several variables and linear algebra
- Over 130 exercises and worked examples
- Self-contained and presents varying viewpoints including Riemannian, complex and algebraic
Sommaire
- Basics on Differential Geometry
- Smooth manifolds;
- Tensor fields on smooth manifolds;
- The exterior derivative;
- Principal and vector bundles;
- Connections;
- Riemannian manifolds;
- Complex and Hermitian Geometry
- Complex structures and holomorphic maps;
- Holomorphic forms and vector fields;
- Complex and holomorphic vector bundles;
- Hermitian bundles;
- Hermitian and Kähler metrics;
- The curvature tensor of Kähler manifolds;
- Examples of Kähler metrics;
- Natural operators on Riemannian and Kähler manifolds;
- Hodge and Dolbeault theory;
- Topics on Compact Kähler Manifolds
- Chern classes;
- The Ricci form of Kähler manifolds;
- The Calabi-Yau theorem;
- Kähler-Einstein metrics;
- Weitzenböck techniques;
- The Hirzebruch-Riemann-Roch formula;
- Further vanishing results;
- Ricci-flat Kähler metrics;
- Explicit examples of Calabi-Yau manifolds;
Caractéristiques techniques
PAPIER | |
Éditeur(s) | Cambridge University Press |
Auteur(s) | Andrei Moroianu |
Collection | London Mathematical Society Student Texts |
Parution | 19/04/2007 |
Nb. de pages | 172 |
Format | 15,5 x 22,5 |
Couverture | Broché |
Poids | 266g |
Intérieur | Noir et Blanc |
EAN13 | 9780521688970 |
ISBN13 | 978-0-521-68897-0 |
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