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The geometry of total curvature on complete open surfaces /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The geometry of total curvature on complete open surfaces // Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka.
作者:	Shiohama, K.
其他作者:	Tanaka, Minoru,
面頁冊數:	1 online resource (ix, 284 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Global differential geometry. -
電子資源:	https://doi.org/10.1017/CBO9780511543159
ISBN:	9780511543159 (ebook)

The geometry of total curvature on complete open surfaces /
Shiohama, K.1940-

The geometry of total curvature on complete open surfaces /Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka. - 1 online resource (ix, 284 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;159. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics.

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.

ISBN: 9780511543159 (ebook)Subjects--Topical Terms:

672282
Global differential geometry.

LC Class. No.: QA670 / .S48 2003

Dewey Class. No.: 516.3/52

The geometry of total curvature on complete open surfaces /
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505 0 $a 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics.
520 $a 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.
650 0 $a Global differential geometry. $3 672282
650 0 $a Curves on surfaces. $3 893597
650 0 $a Riemannian manifolds. $3 580421
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700 1 $a Shioya, Takashi, $d 1963- $e author. $3 1440983
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