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

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.

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

1
Cai M. Lp Willmore functionals. Proc Am Math Soc, 1999, 127: 569-575

DOI

2
Chen B Y. Some conformal invariants of submanifolds and their applications. Boll Un Math Ital, 1974, 10: 380-385

3
Chern S S. Minimal Submanifolds in a Riemannian Manifold. Lawrence: University of Kansas, 1968

4
Chern S S, Carmo M do, Kobayashi S. Minimal submanifolds of a sphere with second fundamental form of constant length. In: Browder F E, ed. Functional Analysis and Related Fields. Berlin: Springer-Verlag, 1970, 59-75

5
Guo Z, Li H Z, Wang C P. The second variation of formula for Willmore submanifolds in Sn. Results in Math, 2001, 40: 205-225

6
Hu Z J, Li H Z. Willmore submanifolds in Riemannian manifolds. In: Bokan N, Djorić M, Fomenko A T, Rakić Z, Wess J, eds. Proceedings of the Workshop, Contem Geom and Related Topics, Belgrade, Yugoslavia, <month>May</month><day>15-21</day>, 2002. Singapore: World Scientific, 2011, 251-275

7
Huisken G. Flow by mean curvature of convex surfaces in to spheres. J Differ Geom, 1984, 20: 237-266

8
Li H Z. Willmore submanifolds in a sphere. Math Research Letters, 2002, 9: 771-790

9
Li H Z, Simon U. Quantization of curvature for compact surfaces in a sphere. Math Z, 2003, 245: 201-216

DOI

10
Pedit F J, Willmore T J. Conformal geometry. Atti Sem Mat Fis UnivModena XXXVI, 1988, 237-245

11
Rigoli M, Salavessa I M. Willmore submanifolds of the Möbius space and a Bernsteintype theorem. Manuscripta Math, 1993, 81: 203-222

DOI

12
Willmore T J. Total Curvature in Riemannian Geometry. New York: Ellis Horwood Ltd, 1982

13
Willmore T J. Riemannian Geometry. Oxford: Oxford Science Pub, Clarendon Press, 1993

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