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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A splitting theorem for higher order parallel immersions
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by Ines Kath and Paul-Andi Nagy PDF
Proc. Amer. Math. Soc. 140 (2012), 2873-2882 Request permission

Abstract:

We consider isometric immersions into space forms having the second fundamental form parallel at order $k$. We show that this class of immersions consists of local products, in a suitably defined sense, of parallel immersions and normally flat immersions of flat spaces.
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Additional Information
  • Ines Kath
  • Affiliation: Institut für Mathematik und Informatik, Ernst-Moritz-Arndt Universität Greifswald, Walther-Rathenau str. 47, 17487 Greifswald, Germany
  • MR Author ID: 99065
  • Email: ines.kath@uni-greifswald.de
  • Paul-Andi Nagy
  • Affiliation: Institut für Mathematik und Informatik, Ernst-Moritz-Arndt Universität Greifswald, Walther-Rathenau str. 47, 17487 Greifswald, Germany
  • MR Author ID: 662210
  • Email: nagyp@uni-greifswald.de
  • Received by editor(s): March 14, 2011
  • Published electronically: December 19, 2011
  • Communicated by: Ken Ono
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 2873-2882
  • MSC (2010): Primary 53B21, 53C42
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11342-X
  • MathSciNet review: 2910773