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: | 9780521450546 |
| Publication date: | 13th November 2003 |
| Author: | Katsuhiro Saga University, Japan Shiohama, Takashi Tohoku University, Japan Shioya, Minoru Tokai University, Japan Tanaka |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 294 pages |
| Series: | Cambridge Tracts in Mathematics |
| Genres: |
Differential and Riemannian geometry Algebraic geometry |