Almost Complex and Complex Structures (Series in Pure Mathematics v. 20)
By: Chuan-Chih Hsiung (author)Hardback
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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 Kahlerian 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.
Riemannian Structures; Almost Complex Structures; Almost Hermitian Structures; Real and Complex Laplacians; Complex Structures; Vanishing Theorems.
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- ID: 9789810217129
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