The Geometry of Total Curvature on Complete Open Surfaces
The Geometry of Total Curvature on Complete Open Surfaces
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DOI：
10.1017/cbo9780511543159
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发表时间：
2003-12
期刊：
影响因子：
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通讯作者：
K. Shiohama;T. Shioya;Minoru Tanaka
中科院分区：
文献类型：
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作者：
K. Shiohama;T. Shioya;Minoru Tanaka
这是关于如何使用微分几何中的一些现代思想来处理和扩展积分几何中的经典结果的独立说明。作者研究了总曲率对完整的非紧黎曼 2 流形的度量结构的影响，尽管他们的工作（其中大部分以前从未以书籍形式出现过）可以扩展到更一般的空间。作者介绍并扩展了许多经典成果。讨论了完全开放表面的紧致化，以及射线的 Busemann 函数。每章都提供了开放性问题，文本配有丰富的插图，旨在帮助读者理解主题并获得关于该主题的直观想法。该方法是独立的，仅假设您具有流形理论的基本知识，因此适合寻求介绍微分几何这一现代领域的研究生和非专业人士。
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.