Geometry of total curvature on complete open surfaces

By:

Shiohama, Katsuhiro

Contributor(s):

Series: Cambridge tracts in mathematics, no. 159Publication details: Cambridge University Press, 2003. Cambridge:Description: ix, 284pp.; hbk; 24cmISBN:

9780521450546

Subject(s):

DDC classification:

516.362 SHI

Summary: 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. https://www.cambridge.org/core/books/geometry-of-total-curvature-on-complete-open-surfaces/47BA349CCB8451D3E24F7813B3B5086A#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	516.362 SHI (Browse shelf(Opens below))	1	Available		031764

Includes index and references

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.

https://www.cambridge.org/core/books/geometry-of-total-curvature-on-complete-open-surfaces/47BA349CCB8451D3E24F7813B3B5086A#fndtn-information

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