Synopsis
The original version of this article was written more than fiveyears ago with S. Z. Shefel',a profound and original mathematician who died in 1984. Sincethen the geometry of surfaces has continued to be enriched with ideas and results. This has required changes and additions, but has not influenced the character of the article, the design ofwhich originated with Shefel'. Without knowing to what extent Shefel' would have approved the changes, I should nevertheless like to dedicate this article to his memory. (Yu. D. Burago) We are trying to state the qualitative questions of the theory of surfaces in Euclidean spaces in the form in which they appear to the authors at present. This description does not entirely correspond to the historical development of the subject. The theory of surfaces was developed in the first place mainly as the 3 theory of surfaces in three-dimensional Euclidean space E ; however, it makes sense to begin by considering surfaces F in Euclidean spaces of any dimension n~ 3. This approach enables us, in particular, to put in a new light some 3 unsolved problems of this developed (and in the case of surfaces in E fairly complete) theory, and in many cases to refer to the connections with the present stage ofdevelopment of the theory of multidimensional submanifolds. The leading question of the article is the problem of the connection between classes of metrics and classes of surfaces in En.
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A volume devoted to the extremely clear and intrinsically beautiful theory of two-dimensional surfaces in Euclidean spaces. The main focus is on the connection between the theory of embedded surfaces and two-dimensional Riemannian geometry, and the influence of properties of intrinsic metrics on the geometry of surfaces.
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Hardcover. Condition: Very Good+. Dust Jacket Condition: No Dust Jacket. (?); (?). The book shows slight bumping to the bottom right of the spine, with a few very minor indents present at the top of the spine. ; *Geometry III - Theory of Surfaces (Volume 48 of the *Encyclopaedia of Mathematical Sciences) by Yu. D. Burago and V. A. Zalgaller provides a detailed study of the geometry of surfaces. This volume covers key concepts like curvature, surface theory, and the behaviour of surfaces in various geometrical contexts, blending both classical and modern approaches to surface geometry. ; 16.9 x 23.9 x 2 cm ; 256, (2) pages. Seller Inventory # 62351
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