Kähler Metric and Moduli Spaces

Kähler Metric and Moduli Spaces, Volume 18-II covers survey notes from the expository lectures given during the seminars in the academic year of 1987 for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential equations. The book discusses basic facts on Einstein metrics in complex geometry; Einstein-Kähler metrics with positive or non-positive Ricci curvature; Yang-Mills connections; and Einstein-Hermitian metrics. The text then describes the tangent sheaves of minimal varieties; Ricci-Flat Kähler metrics on affine algebraic manifolds; and degenerations of Kähler-Einstein. The moduli of Einstein metrics on a K3 surface and degeneration of Type I and the uniformization of complex surfaces are also considered. Mathematicians and graduate students taking differential and analytic geometry will find the book useful.

(1) Einstein Metrics in Complex Geometry: An Introduction

(2) Einstein-Kähler Metrics with Positive Ricci Curvature

(3) Einstein-Kähler Metrics with Non-Positive Ricci Curvature

(3-a) On the Tangent Sheaves of Minimal Varieties

(3-b) Einstein Kähler Metrics on Negative Ricci Curvature on Open Kähler Manifolds

(3-c) Ricci-Flat Kähler Metrics on Affine Algebraic Manifolds and Degenerations of Kähler-Einstein K3 Surfaces

(3-d) Compact Ricci-Flat Kähler Manifolds

(3-e) Moduli of Einstein Metrics on K3-Surfaces and Degeneration of Type I

(3-f) Uniformization of Complex Surfaces

(4) Yang-Mills Connections and Einstein-Hermitian Metrics