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A splitting theorem for higher order parallel immersions


Authors: Ines Kath and Paul-Andi Nagy
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
Published electronically: December 19, 2011
MathSciNet review: 2910773
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Abstract | References | Similar Articles | Additional Information

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
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
Email: nagyp@uni-greifswald.de

DOI: https://doi.org/10.1090/S0002-9939-2011-11342-X
Keywords: Submanifold, higher order parallel fundamental form, splitting theorems
Received by editor(s): March 14, 2011
Published electronically: December 19, 2011
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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