Lectures on Kähler Geometry (London Mathematical Society Student Texts Book 69) 1st Edition by Andrei Moroianu (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Complete, concise to begin studying Complex Manifolds

⭐This is an excellent introduction to complex geometry, it is clear, well written and accessible for beginners. I think the choice of topics is excellent and the order in which they appear is also good. This book is well balanced, it presents the material necessary to understand advanced topics in a quick and efficient way. It is very concise, so you will not find a deep coverage of some topics such as Hodge and Dolbeault theory or a lot of examples, in this case I would recommend to supplement this book with Complex Differential Geometry by Fangyang Zheng, AMS or Werner Ballmann Lectures on Kahler manifolds or Huybrechts’book.

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