Archiv der Mathematik

, Volume 110, Issue 5, pp 523–531 | Cite as

Einstein submanifolds with parallel mean curvature

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Abstract

We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to Dajczer and Tojeiro (Tohoku Math J (2) 45:43–49, 1993) for isometric immersions of Riemannian manifolds with constant sectional curvature.

Keywords

Einstein submanifolds Parallel mean curvature Flat normal bundle Principal normals 

Mathematics Subject Classification

Primary 53B25 Secondary 53C40 53C42 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece

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