Lectures on K}}hler Geometry [Paperback]

This graduate text provides a concise and self-contained introduction to K?hler geometry.K?hler geometry is of substantial interest to both mathematicians and physicists and this graduate text provides a self-contained introduction to the subject. Topics discussed include complex manifolds and holomorphic vector bundles; K?hler manifolds and Hodge and Dolbeault theories; compact K?hler manifolds and a proof of the famous K?hler identities.K?hler geometry is of substantial interest to both mathematicians and physicists and this graduate text provides a self-contained introduction to the subject. Topics discussed include complex manifolds and holomorphic vector bundles; K?hler manifolds and Hodge and Dolbeault theories; compact K?hler manifolds and a proof of the famous K?hler identities.K?hler 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. K?hler 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 K?hler identities. The final part of the text studies several aspects of compact K?hler manifolds: the Calabi conjecture, Weitzenb?ck techniques, CalabiYau 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.Introduction; Part I. Basics on Differential Geometry: 1. Smooth manifolds; 2. Tensor fields on smooth manifolds; 3. The exterior derivative; 4. Principal and vector bundles; 5. Connections; 6. Riemannian manifolds; Partl“T