Titlebook: Geometry III; Theory of Surfaces Yu. D. Burago,V. A. Zalgaller Book 1992 Springer-Verlag Berlin Heidelberg 1992 Differential Geometry.Diffe

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Local Theory of Bendings of Surfaces,hy and Gauss. After it was discovered that on surfaces there is an “intrinsic geometry” that does not depend on the external form of the surface, there naturally arose the question of the possibility of deforming the surface, preserving its intrinsic geometry. Consideration of isometric immersions (

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0938-0396 n 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 cha

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Surfaces of Negative Curvature, and Lychagin (1988), Alekseevskij, Vinberg and Solodovnikov (1988), Burago and Shefel’ (1989), and Sabitov (1989b), we repeat certain facts in the text that are already reflected in these surveys. However, these repetitions are comparatively small.

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Local Theory of Bendings of Surfaces,e naturally arose the question of the possibility of deforming the surface, preserving its intrinsic geometry. Consideration of isometric immersions (or, as we say, realizations) of abstractly given Riemannian metrics also leads to the problem of bendings of surfaces as to some problem about the uniqueness or non-uniqueness of an immersion.

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Christopher J. Lucase., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty