Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 5: 871 - 886

DOI: https://doi.org/10.1007/s11464-011-0140-y

RESEARCH ARTICLE

F-Willmore submanifold in space forms

  • Jin LIU ,
  • Huaiyu JIAN
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  • Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 31 Jan 2011

Accepted date: 29 Mar 2011

Published date: 01 Oct 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We introduce an F-Willmore functional of submanifold in space forms, which generalizes the well-known Willmore functional. Its critical point is called the F-Willmore submanifold, for which the variational equation and Simons’ type integral inequality are obtained.

Key words： Mean curvature; Willmore submanifold; Simons’ type integral inequality

Cite this article

Jin LIU , Huaiyu JIAN . F-Willmore submanifold in space forms[J]. Frontiers of Mathematics in China, 2011 , 6(5) : 871 -886 . DOI: 10.1007/s11464-011-0140-y

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