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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces
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by Gil Solanes PDF
Trans. Amer. Math. Soc. 358 (2006), 1105-1115 Request permission

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
  • 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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 1105-1115
  • MSC (2000): Primary 53C65
  • DOI: https://doi.org/10.1090/S0002-9947-05-03828-6
  • MathSciNet review: 2187647