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Author: Chuan-chih Hsiung
Publisher: World Scientific
ISBN: 9814518107
Category : Mathematics
Languages : en
Pages : 328
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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 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.
Author: Chuan-chih Hsiung
Publisher: World Scientific
ISBN: 9814518107
Category : Mathematics
Languages : en
Pages : 328
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 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.
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: 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: 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: Chuan-Chih Hsiung
Publisher: World Scientific
ISBN: 9789812810618
Category : Mathematics
Languages : en
Pages : 728
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Book Description
This invaluable book contains selected papers of Prof Chuan-Chih Hsiung, renowned mathematician in differential geometry and founder and editor-in-chief of a unique international journal in this field, the Journal of Differential Geometry . During the period of 1935OCo1943, Prof Hsiung was in China working on projective differential geometry under Prof Buchin Su. In 1946, he went to the United States, where he gradually shifted to global problems. Altogether Prof Hsiung has published about 100 research papers, from which he has selected 64 (in chronological order) for this volume. Contents: Projective Differential Geometry of a Pair of Plane Curves; A Projective Invariant of a Certain Pair of Surfaces; Affine Invariants of a Pair of Hypersurfaces; A Theorem on Surfaces with a Closed Boundary; Some Uniqueness Theorem on Riemannian Manifolds with Boundary; On the Group of Conformal Transformations of a Compact Riemannian Manifold; Minimal Immersions in Riemannian Spheres; A Remark on Pinched Manifolds with Boundary; Nonexistence of a Complex Structure on the Six-Sphere; Some Conditions for a Complex Structure; and other papers. Readership: Researchers in differential geometry."
Author: Dong Hoon Lee
Publisher: CRC Press
ISBN: 1420035452
Category : Mathematics
Languages : en
Pages : 229
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Book Description
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects. The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts
Author: Raymond O. Wells
Publisher: Springer Science & Business Media
ISBN: 0387738916
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
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: Klaus Fritzsche
Publisher: Springer Science & Business Media
ISBN: 146849273X
Category : Mathematics
Languages : en
Pages : 406
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Book Description
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
