Recent Topics in Differential and Analytic Geometry

✍ Scribed by T. Ochiai

• Publisher: Academic Press
• Year: 1991
• Tongue: English
• Leaves: 445
• Series: Advanced Studies in Pure Mathematics
• Category: Library

✦ Synopsis

Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.

Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind.

This book is a valuable resource for graduate students and pure mathematicians.

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Advanced Studies in Pure Mathematics, Pages v-vi
Foreword, Page vii, H. MORIKAWA, M. NAGATA
Preface to the Present Volume, Page ix, T. OCHIAI
CONTENTS OF VOLUME 18-II, Page xiii
Topics in Complex Differential Geometry, Pages 1-141, Ngaiming Mok
Hausdorff Convergence of Riemannian Manifolds and Its Applications, Pages 143-238, Kenji Fukaya
Compact Kähler Manifolds with Parallel Ricci Tensor, Pages 239-249, Ichiro Enoki
Eta Invariants and Automorphisms of Compact Complex Manifolds, Pages 251-270, Akito Futaki, Kenji Tsuboi
Poincaré Bundle and Chern Classes, Pages 271-281, Mitsuhiro Itoh
Harmonic Functions with Growth Conditions on a Manifold of Asymptotically Nonnegative Curvature II, Pages 283-301, Atsushi Kasue
Homogeneous Einstein Metrics On Certain Kähler C-Spaces, Pages 303-320, Masahiro Kimura
An Application of Kähler-Einstein Metrics to Singularities of Plane Curves, Pages 321-326, Ryoichi Kobayashi
On Rotationally Symmetric Hamilton's Equation for Kähler-Einstein Metrics, Pages 327-337, Norihito Koiso
An Algebraic Character associated with the Poisson Brackets, Pages 339-358, Toshiki Mabuchi
Compactification of the Moduli Space of Einstein-Kähler Orbifolds, Pages 359-384, Toshiki Mabuchi
Self-Duality of ALE Ricci-Flat 4-Manifolds and Positive Mass Theorem, Pages 385-396, Hiraku Nakajima
Compactification of Moduli Spaces of Einstein-Hermitian Connections for Null-Correlation Bundles, Pages 397-416, Takashi Nitta
Einstein-Kähler Metrics on Minimal Varieties of General Type and an Inequality between Chern Numbers, Pages 417-443, Ken-ichi Sugiyama