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Home > Mathematics and Science books > Mathematics > Geometry > Differential and Riemannian geometry > Geometry III: Theory of Surfaces(48 Encyclopaedia of Mathematical Sciences)
Geometry III: Theory of Surfaces(48 Encyclopaedia of Mathematical Sciences)

Geometry III: Theory of Surfaces(48 Encyclopaedia of Mathematical Sciences)


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About the Book

The theory of two-dimensional surfaces in Euclidean spacesis remarkably rich in deep results and applications, forexample in the theory of non-linear partial differentialequations, physics and mechanics. This theory has greatclarity and intrinsic beauty, and differs in many respectsfrom the theory of multidimensional submanifolds. A separatevolume of the Encyclopaedia is therefore devoted tosurfaces. It is concerned mainly with the connection betweenthe theory of embedded surfaces and two-dimensionalRiemannian geometry (and its generalizations), and, aboveall, with the question of the influence of properties ofintrinsic metrics on the geometry of surfaces.In the first article Yu.D.Burago and S.Z.Shefel' give anextended survey of surfaces from a non-traditional viewpointstressing the connection between classes of metrics andclasses of surfaces in En. A number of conjectures areincluded.The article of E.R.Rozendorn considers the state of the artof the still incomplete theory of the geometry of surfacesof negative curvature in three-dimensional Euclidean space,and the article of I.Kh.Sabitov considers subtle questionsof local bendability and rigidity ofsurfaces.These articles reflect the development of the results ofN. V.Efimov and also include statements of unsolved problems.

Table of Contents:
I. The Geometry of Surfaces in Euclidean Spaces.- II. Surfaces of Negative Curvature.- III. Local Theory of Bendings of Surfaces.- Author Index.


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Product Details
  • ISBN-13: 9783540533771
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 258
  • Returnable: N
  • Sub Title: Theory of Surfaces
  • ISBN-10: 354053377X
  • Publisher Date: 08 Oct 1992
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Series Title: 48 Encyclopaedia of Mathematical Sciences
  • Width: 155 mm


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Geometry III: Theory of Surfaces(48 Encyclopaedia of Mathematical Sciences)
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