Riemannian Geometry In An Orthogonal Frame

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Vladislav V Goldberg (New Jersey Inst Of Tech, Usa) Shiing-shen Chern (Nankai Univ, China)

Riemannian Geometry In An Orthogonal Frame

Vladislav V Goldberg (New Jersey Inst Of Tech, Usa), Shiing-shen Chern (Nankai Univ, China), Vladislav V. Goldberg

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Russian

World Scientific Publishing Co Pte Ltd
11 December 2001

Mathematics & Sciences; Differential & Riemannian geometry; Topology

"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."

Foreword by: Shiing-shen Chern (Nankai Univ China)
Translated by: Vladislav V Goldberg (New Jersey Inst Of Tech Usa), Vladislav V. Goldberg
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Dimensions: Height: 230mm, Width: 152mm, Spine: 15mm
Weight: 408g
ISBN: 9789810247478
ISBN 10: 9810247478
Pages: 280
Publication Date: 11 December 2001
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Method of moving frames; integration of systems of Pfaffian differential equations; the fundamental theorem of metric geometry; tensor analysis; locally Euclidean Riemannian manifolds; osculating Euclidean space; Riemannian curvature of a manifold; variational problems for geodesics; geodesic surfaces; lines in a Riemannian manifold; forms of Laguerre and Darboux; and other papers.