The Geometry of Total Curvature on Complete Open Surfaces (Cambridge Tracts in Mathematics)
Publisher: Cambridge University Press
Published: December 22, 2003
Language: eng
Format: Hardcover
Number of pages: 294
ISBN-13: 9780521450546
Subjects: Algebraic geometry; Differential & Riemannian geometry; Mathematics; Geometry - Algebraic; Science/Mathematics; Riemannian manifolds; Mathematics / Applied; Curves on surfaces; Geometry - Differential; Global differential geometry
First sentence: We introduce the basic tools of Riemannian geometry that we shall need assuming that readers already know basic facts about manifolds.
Description: 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.