The Geometry of Total Curvature on Complete Open Surfaces

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Katsuhiro Shiohama (Saga University, Japan) Takashi Shioya (Tohoku University, Japan)

The Geometry of Total Curvature on Complete Open Surfaces

Katsuhiro Shiohama (Saga University, Japan), Takashi Shioya (Tohoku University, Japan), Minoru Tanaka (Tokai University, Japan)

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English

Cambridge University Press
17 February 2004

Differential & Riemannian geometry; Algebraic geometry

Series: Cambridge Tracts in Mathematics

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.

By: Katsuhiro Shiohama (Saga University Japan), Takashi Shioya (Tohoku University, Japan), Minoru Tanaka (Tokai University, Japan)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 159
Dimensions: Height: 236mm, Width: 161mm, Spine: 21mm
Weight: 535g
ISBN: 9780521450546
ISBN 10: 0521450543
Series: Cambridge Tracts in Mathematics
Pages: 294
Publication Date: 17 February 2004
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active