Goldberg Vladislav V's Books

Theory of Multicodimensional (n+1)-Webs

By: Vladislav V. Goldberg

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Theory of Multicodimensional (n+1)-Webs

By: Vladislav V. Goldberg

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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486

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400930135

ISBN 13

9789400930131

Conformal Differential Geometry and Its Generalizations

By: Maks A. Akivis,Vladislav V. Goldberg

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Conformal Differential Geometry and Its Generalizations

By: Maks A. Akivis,Vladislav V. Goldberg

Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory. Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structures of all possible signatures. * Considers the analytic and differential geometry of Grassmann and almost Grassmann structures. * Draws connections between almost Grassmann structures and web theory. Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures. After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context. The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings. This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics.

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404

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030885

ISBN 13

9781118030882

Tensor Calculus with Applications

By: Maks A?zikovich Akivis,Vladislav V. Goldberg

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Tensor Calculus with Applications

By: Maks A?zikovich Akivis,Vladislav V. Goldberg

This textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, sincesuch tensors are important in applications to physics and engineering. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book p

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Page Count

384

Publisher

World Scientific

Published Date

ISBN 10

9812385061

ISBN 13

9789812385062

Differential Geometry of Varieties with Degenerate Gauss Maps

By: Maks A. Akivis,Vladislav V. Goldberg

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Differential Geometry of Varieties with Degenerate Gauss Maps

By: Maks A. Akivis,Vladislav V. Goldberg

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

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272

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387215115

ISBN 13

9780387215112

Projective Differential Geometry of Submanifolds

By: M.A. Akivis,V.V. Goldberg

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Projective Differential Geometry of Submanifolds

By: M.A. Akivis,V.V. Goldberg

In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations.Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.

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Page Count

375

Publisher

Elsevier

Published Date

ISBN 10

0080887163

ISBN 13

9780080887166

Differential Geometry of Varieties with Degenerate Gauss Maps

By: Maks A. Akivis,Vladislav V. Goldberg

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Differential Geometry of Varieties with Degenerate Gauss Maps

By: Maks A. Akivis,Vladislav V. Goldberg

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Page Count

282

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387404635

ISBN 13

9780387404639

Book's by Goldberg Vladislav V

Theory of Multicodimensional (n+1)-Webs

Theory of Multicodimensional (n+1)-Webs

Conformal Differential Geometry and Its Generalizations

Conformal Differential Geometry and Its Generalizations

Tensor Calculus with Applications

Tensor Calculus with Applications

Differential Geometry of Varieties with Degenerate Gauss Maps

Differential Geometry of Varieties with Degenerate Gauss Maps

Projective Differential Geometry of Submanifolds

Projective Differential Geometry of Submanifolds

Differential Geometry of Varieties with Degenerate Gauss Maps

Differential Geometry of Varieties with Degenerate Gauss Maps

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