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Transactions of the American Mathematical Society

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Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces


Author: Gil Solanes
Journal: Trans. Amer. Math. Soc. 358 (2006), 1105-1115
MSC (2000): Primary 53C65
DOI: https://doi.org/10.1090/S0002-9947-05-03828-6
Published electronically: April 22, 2005
MathSciNet review: 2187647
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.


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Additional Information

Gil Solanes
Affiliation: Institut für Geometrie und Topologie, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Address at time of publication: Institut de Mathématiques de Bourgogne, 9 Avénue Alain Savary – BP 47870, 21078 Dijon Cedex, France
Email: solanes@mathematik.uni-stuttgart.de, solanes@topolog.u-bourgogne.fr

DOI: https://doi.org/10.1090/S0002-9947-05-03828-6
Keywords: Integral geometry, total curvature
Received by editor(s): April 15, 2004
Published electronically: April 22, 2005
Additional Notes: This work was partially supported by MECD grant EX2003-0987 and MCYT grant BMF2003-03458
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.