| 概要 |
Kahler geometry is a beautiful and intriguing area of mathematics, of substantial research interest both to mathematicians and physicists. This self-contained graduate text provides a concise and acce...sible 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. Kahler 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 Kahler identities. The final part of the text studies several aspects of compact Kahler manifolds: the Calabi conjecture, Weitzenbock techniques, Calabi-Yau manifolds, and divisors. Each section of the book ends 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. Book jacket.
Kahler geometry is a beautiful and intriguing area of mathematics, of substantial research interest both to 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. Kahler 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 Kahler identities. The final part of the text studies several aspects of compact Kahler manifolds: the Calabi conjecture, Weitzenbock techniques, Calabi-Yau manifolds, and divisors. Each section of the book ends 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. Book jacket.続きを見る
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