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Author: C. C. Hsiung
Publisher: World Scientific
ISBN: 9789810217129
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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 Khlerian 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.
Author: C. C. Hsiung
Publisher: World Scientific
ISBN: 9789810217129
Category : Mathematics
Languages : en
Pages : 336
Get Book Here
Book Description
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 Khlerian 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.
Author: K. Kodaira
Publisher: Springer Science & Business Media
ISBN: 1461385903
Category : Mathematics
Languages : en
Pages : 476
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Book Description
This book is an introduction to the theory of complex manifolds and their deformations. Deformation of the complex structure of Riemann surfaces is an idea which goes back to Riemann who, in his famous memoir on Abelian functions published in 1857, calculated the number of effective parameters on which the deformation depends. Since the publication of Riemann's memoir, questions concerning the deformation of the complex structure of Riemann surfaces have never lost their interest. The deformation of algebraic surfaces seems to have been considered first by Max Noether in 1888 (M. Noether: Anzahl der Modulen einer Classe algebraischer Fliichen, Sitz. K6niglich. Preuss. Akad. der Wiss. zu Berlin, erster Halbband, 1888, pp. 123-127). However, the deformation of higher dimensional complex manifolds had been curiously neglected for 100 years. In 1957, exactly 100 years after Riemann's memoir, Frolicher and Nijenhuis published a paper in which they studied deformation of higher dimensional complex manifolds by a differential geometric method and obtained an important result. (A. Fr61icher and A. Nijenhuis: A theorem on stability of complex structures, Proc. Nat. Acad. Sci., U.S.A., 43 (1957), 239-241).
Author: Daniel Huybrechts
Publisher: Springer Science & Business Media
ISBN: 9783540212904
Category : Computers
Languages : en
Pages : 336
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Book Description
Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
Author: Kouei Sekigawa
Publisher: World Scientific
ISBN: 9814549843
Category :
Languages : en
Pages : 234
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Book Description
The geometry of almost complex structures is fundamentally concerned with complex analysis and also mathematical physics. In view of the increasing interest in almost complex structures, this volume will be useful in future studies of geometry and complex analysis, and related fields.
Author: Shiing-shen Chern
Publisher: Springer Science & Business Media
ISBN: 1468493442
Category : Mathematics
Languages : en
Pages : 158
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Book Description
From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#
Author: Andrei Moroianu
Publisher: Cambridge University Press
ISBN: 1139463004
Category : Mathematics
Languages : en
Pages : 4
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Book Description
Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Author: Simon Brendle
Publisher: American Mathematical Soc.
ISBN: 0821849387
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Deals with the Ricci flow, and the convergence theory for the Ricci flow. This title focuses on preserved curvature conditions, such as positive isotropic curvature. It is suitable for graduate students and researchers.
Author: James Ryan Brown
Publisher:
ISBN:
Category : Almost complex manifolds
Languages : en
Pages :
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Book Description
We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP3. This is motivated by the long standing question in differential geometry of whether or not the six sphere S6 admits an integrable almost-complex structure. An affirmative answer to this question would imply the existence of many exotic complex structures on CP3. It is known that CP3 admits many topologically different almost-complex structures, but it is unknown whether or not CP3 admits an integrable almost-complex structure other that the standard Kähler structure. In this manuscript we give lower bounds on the Hodge numbers of hypothetical exotic structures on CP3 and a necessary condition for the Frölicher spectral sequence to degenerate at the second level. We also give topological constraints on the classes of hypothetical exotic complex structures which areC*-symmetric. We give restrictions on the fixed point sets of such C* actions.
Author: Max Karoubi
Publisher: Springer Science & Business Media
ISBN: 3540798900
Category : Mathematics
Languages : en
Pages : 337
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Book Description
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Author: Michele Audin
Publisher: Birkhäuser
ISBN: 3034885083
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.
