Almost Complex And Complex Structures

Chuan-chih Hsiung

• Publisher: World Scientific
• Year: 1995
• Print ISBN: 9789810217129, 9789810217129
• eBook ISBN: 9789812831941
• Topic: Mathematics
• Subtopic: Analytic Geometry
• Index: Mathematics

This book gives a self-contained fundamental study of the subject. Besides the following special features it contains the author's detailed solution to the long-standing unsolved problem in the theory of complex manifolds: Does there exist a complex structure on the six-sphere? The special features of the book are: a classification of almost complex (and similarly, almost Hermitian) structures together with inclusion relations; discussions about various known almost Hermitian structures; a necessary and sufficient condition for a general almost Hermitian manifold to have constant holomorphic sectional (or bisectional) curvature and similar conditions for various special almost Hermitian manifolds; some complex Laplacians together with some of their relationships with the real Laplacian; the spectral geometry of Riemannian manifolds and some general almost Hermitian manifolds including Kählerian manifolds as a special case; conditions for an almost complex structure to be a complex structure; some vanishing theorems for Riemannian and almost Hermitian manifolds.

Table of contents

• Contents
• Preface
• I. RIEMANNIAN STRUCTURES
• II. ALMOST COMPLEXSTRUCTURES
• III. ALMOST HERMITIANSTRUCTURES
• IV. THE REAL LAPLACIAN
• V. COMPLEX LAPLACIANS
• VI. COMPLEX STRUCTURES
• VII. VANISHING THEOREMS
• Bibliography
• Index