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Geometry IV : Non-regular Riemannian Geometry - IU.G. Reshetniak

Geometry IV

Non-regular Riemannian Geometry

By: IU.G. Reshetniak (Editor), IU.G.Reshetniak (Editor), Eric Primrose (Translator)

Hardcover Published: 1st October 1993
ISBN: 9783540547013
Number Of Pages: 252

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This volume of the Encyclopaedia contains two articles,which give a survey of modern research into non-regularRiemannian geometry, carried out mostly by Russianmathematicians.The first article written by Reshetnyak is devoted to thetheory of two-dimensional Riemannian manifolds of boundedcurvature. Concepts of Riemannian geometry, such as the areaandintegral curvature of a set, and the length and integralcurvature of a curve are also defined for these manifolds.Some fundamental results of Riemannian goemetry like theGauss-Bonnet formula are true in the more general caseconsidered in the book.The second article by Berestovskij and Nikolaev is devotedto the theory of metric spaces whose curvature lies betweentwo given constants. The main result is that these spacesare infact Riemannian. This result has importantapplications in global Riemanniangeometry.Both parts cover topics, which have not yet been treated inmonograph form. Hence the book will be immensely useful tograduate students and researchers in geometry, in particularRiemannian geometry.

Two-Dimensional Manifolds of Bounded Curvature
Multidimensional Generalized Riemannian Spaces
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540547013
ISBN-10: 3540547010
Series: Encyclopaedia of Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 252
Published: 1st October 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.5
Weight (kg): 1.21