Maks A. Akivis's Books

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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Page Count

272

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387215115

ISBN 13

9780387215112

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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Page Count

404

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030885

ISBN 13

9781118030882

Elie Cartan (1869-1951)

By: Maks Aĭzikovich Akivis,Boris Abramovich Rozenfelʹd

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Elie Cartan (1869-1951)

By: Maks Aĭzikovich Akivis,Boris Abramovich Rozenfelʹd

This book describes the life and achievements of the great french mathematician, Élie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential geometry, as well as later developments stemming from his ideas. The volume includes a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.

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Page Count

372

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184587X

ISBN 13

9780821845875

Tensor Calculus With Applications

By: Vladislav V Goldberg,Maks A Akivis

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Tensor Calculus With Applications

By: Vladislav V Goldberg,Maks A Akivis

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider 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.With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis.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 and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.

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Page Count

381

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

981310225X

ISBN 13

9789813102255

Book's by Maks A. Akivis

Differential Geometry of Varieties with Degenerate Gauss Maps

Differential Geometry of Varieties with Degenerate Gauss Maps

Conformal Differential Geometry and Its Generalizations

Conformal Differential Geometry and Its Generalizations

Elie Cartan (1869-1951)

Elie Cartan (1869-1951)

Tensor Calculus With Applications

Tensor Calculus With Applications

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