Hidden Bibliographic Details
| Other authors / contributors: | Finikov, S. P. (Sergeĭ Pavlovich), 1883-1964.
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| ISBN: | 9789812799715
9812799710
1281948039
9781281948038
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| Notes: | Translated from the 1960 Russian ed., which was translated and edited from original lecture notes by S.P. Finikov as, Rimanova geometriya v orthogonalʹnom repere.
Includes bibliographical references and index.
Print version record.
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| Summary: | Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition.
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| Other form: | Print version: Cartan, Elie, 1869-1951. Rimanova geometrii︠a︡ v ortogonalʹnom repere. English. Riemannian geometry in an orthogonal frame. River Edge, NJ : World Scientific, ©2001 981024746X 9789810247461
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