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.References
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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