The Geometry of Total Curvature on Complete Open Surfaces (Cambridge Tracts in Mathematics)
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This independent account of modern ideas in differential geometry shows how they can be used to understand and extend classical results in integral geometry. The authors explore the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, although their work can be extended to more general spaces. Each chapter features open problems, making the volume a suitable learning aid for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
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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.
--This text refers to the
Digital
edition.
The Geometry of Total Curvature on Complete Open Surfaces (Cambridge Tracts in Mathematics),Katsuhiro Shiohama,Takashi Shioya,Minoru Tanaka,B. Bollobas,W. Fulton,A. Katok,F. Kirwan,P. Sarnak,B. Simon,Cambridge University Press,0521450543,Curves on surfaces,Geometry - Algebraic,Geometry - Differential,Global differential geometry,Mathematics,Riemannian manifolds,Science/Mathematics,Algebraic geometry,Differential & Riemannian geometry,Mathematics / Applied
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