Geometry III

Theory of Surfaces

Yu.D. Burago, V.A. Zalgaller, V.A. Zalgaller , Eric Primrose

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Russian

Springer Verlag
01 June 1992

Mathematics & Sciences; Differential & Riemannian geometry

Series: Encyclopaedia of Mathematical Sciences

Summary
Details

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.

Edited by: Yu.D. Burago, V.A. Zalgaller, V.A. Zalgaller
Translated by: Eric Primrose
Imprint: Springer Verlag
Country of Publication: Germany
Volume: v. 48
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 1.230kg
ISBN: 9783540533771
ISBN 10: 354053377X
Series: Encyclopaedia of Mathematical Sciences
Pages: 263
Publication Date: 01 June 1992
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active