Geometry IV

Non-regular Riemannian Geometry

By: Yu.G. Reshetnyak (Editor), E. Primrose (Translator), V.N. Berestovskij (Contribution by)

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Hardcover | 21 October 1993

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264 Pages

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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.

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Non-Fiction Mathematics Geometry Non-Euclidean Geometry Differential & Riemannian Geometry Analytic Geometry

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Published: 1st December 2010

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Two-Dimensional Manifolds of Bounded Curvature
Multidimensional Generalized Riemannian Spaces
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Geometry IV

Non-regular Riemannian Geometry

At a Glance

Hardcover

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You Can Find This Book In

Other Editions and Formats

Paperback

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