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Recent topics in differential and analytic geometry
1 online resource (462 pages) : illustrations
Front Cover; Recent Topics in Differential and Analytic Geometry; Copyright Page; Foreword; Preface to the Present Volume; Table of Contents; CONTENTS OF VOLUME 18-II; Part I; Section A: Topics in Complex Differential Geometry; TABLE OF CONTENTS; Lecture I. Harmonic Mappings and Holomorphic Foliations; (1.1) Some generalities about bounded symmetric domains; (1.2) Some remarks on quotients of bounded symmetric domains; (1.3) Local rigidity for compact quotients of bounded symmetric domains; (1.4) Mostow's Strong Rigidity Theorem.
(1.5) Harmonic mappings into compact manifolds of non-positive curvature(1.6) Siu's Strong Rigidity Theorem for Kähler manifolds; (1.7) Irreducible compact quotients of the polydisc; (1.8) Holomorphic foliations arising from harmonic maps into irreducible compact quotients of the polydisc; (1.9) Strong rigidity for quotients of the ball of finite volume; (1.10) Strong rigidity for irreducible quotients of the polydisc of finite volume; Lecture II. Uniformization of Compact Kähler Manifolds of Nonnegative Curvature; (2.1) Hermitian symmetric manifolds of compact type.
(2.2) Bochner formulas and the maximum principle on tensors(2.3) Existence of rational curves and the Hartshorne conjecture; (2.4) Stable harmonic mappings and the Frankel Conjecture; (2.5) Evolution of Kähler metric by the parabolic Einstein equation; (2.6) Compact Kähler-Einstein manifolds of non-negative holomorphic bisectional curvature; (2.7) Characterization of locally symmetric spaces of rank d"2 by the holonomy group; (2.8) The space of minimal rational curves on Hermitian symmetric manifolds of compact type.
(2.9) Holonomy-invariance of the space of tangents to minimal rational curvesLecture III. Compactification of Complete Kähler Manifolds of Positive Curvature; The Frankel Conjecture for open manifolds; (3.2) Techniques of L2-estimate of ∂ for the embedding problem; (3.3) Siegel's Theorem for the field of rational functions; (3.4) L2-estimates for the ideal problem and quasi-surjectivity; (3.5) Desingularizing the quasi-surjective embedding Fo; (3.6) Completion to a proper holomorphic embedding; (3.7) Embedding complete Kähler manifolds of positive Ricci curvature
(3.8) Characterization of affine-algebraic varietiesLecture IV. Compactification of Complete Kähler-Einstein Manifolds of Finite Volume; (4.1) Compactification of arithmetic quotients of bounded symmetric domains and generalizations; (4.2) Siegel's Theorem on pseudoconcave manifolds; (4.3) Embedding certain pseudoconcave manifolds; (4.4) Scheme for compactifying certain pseudoconcave manifolds of negative Ricci curvature; (4.5) Existence theorems on complete Kähler-Einstein metrics on non-compact manifolds; (4.6) L2-Riemann-Roch inequality of Nadel-Tsuji.
Includes bibliographical references at the end of each chapters.
Tokyo, Japan : Kinokuniya Company Ltd., ©1990
Advanced studies in pure mathematics (Tokyo, Japan) ; 18-I