By Andrei Moroianu
Kähler geometry is a gorgeous and exciting region of arithmetic, of considerable learn curiosity to either mathematicians and physicists. This self-contained graduate textual content presents a concise and obtainable creation to the subject. The ebook starts with a assessment of simple differential geometry, ahead of relocating directly to an outline of complicated manifolds and holomorphic vector bundles. Kähler manifolds are mentioned from the viewpoint of Riemannian geometry, and Hodge and Dolbeault theories are defined, including an easy facts of the recognized Kähler identities. the ultimate a part of the textual content stories numerous elements of compact Kähler manifolds: the Calabi conjecture, Weitzenböck concepts, Calabi-Yau manifolds, and divisors. All sections of the publication finish with a chain of routines and scholars and researchers operating within the fields of algebraic and differential geometry and theoretical physics will locate that the booklet presents them with a legitimate knowing of this conception.