The Geometry of Total Curvature on Complete Open Surfaces ebook Shiohama, Katsuhiro, Shioya, Takashi, Tanaka, Minoru Diesel eBooks

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Home > Education > Mathematics > Geometry - General > Geometry - Algebraic > The Geometry of Total Curvature on Complete Open Surfaces-eBook

The Geometry of Total Curvature on Complete Open Surfaces

Shiohama, Katsuhiro, Shioya, Takashi, Tanaka, Minoru

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The Geometry of Total Curvature on Complete Open Surfaces

This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

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Title of ebook: The Geometry of Total Curvature on Complete Open Surfaces
ISBN: 9780511059155
Publisher: Cambridge University Press
Internet download file size: 1657 kb
Pages: 294
Released online for download: 11-12-1999
Author of eBook: Shiohama, Katsuhiro
Author of eBook: Shioya, Takashi
Author of eBook: Tanaka, Minoru