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Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces
Author(s):
Gil
Solanes
Journal:
Trans. Amer. Math. Soc.
358
(2006),
1105-1115.
MSC (2000):
Primary 53C65
Posted:
April 22, 2005
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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.
References:
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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:
10.1090/S0002-9947-05-03828-6
PII:
S 0002-9947(05)03828-6
Keywords:
Integral geometry,
total curvature
Received by editor(s):
April 15, 2004
Posted:
April 22, 2005
Additional Notes:
This work was partially supported by MECD grant EX2003-0987 and MCYT grant BMF2003-03458
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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