Article

# F-Willmore submanifold in space forms

Frontiers of Mathematics in China (Impact Factor: 0.5). 10/2011; 6(5):871-886. DOI: 10.1007/s11464-011-0140-y

**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.

KeywordsMean curvature–Willmore submanifold–Simons’ type integral inequality

is called the F-Willmore submanifold, for which the variational equation and Simons’ type integral inequality are obtained.

KeywordsMean curvature–Willmore submanifold–Simons’ type integral inequality

- TAIWANESE JOURNAL OF MATHEMATICS 01/2013; 17(1):109-131. · 0.62 Impact Factor
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**ABSTRACT:**Let M2 be a compact F-Willmore surface in the n-dimensional space form Nn(c) of constant curvature c. Denote by the trace free part of the second fundamental form and by H the mean curvature vector of M2. Let Φ be the square of the length of and. If F'(Φ) ≥ 0, then. The constant function K(n) = 1 when n = 3 and when n ≥ 4.Similarly. We also prove the following: If M2is a compact Willmore surface in the n-dimensional space form Nn (c). Then where C(n) = 2 when n = 3 and when n ≥ 4. If then either Φ = 0 and M is totally umbilicalsphere, or. In the latter case, either M is the Cliffordtorus in S3 of NnTAIWANESE JOURNAL OF MATHEMATICS 01/2013; 17(1). DOI:10.11650/tjm.17.2013.1840 · 0.62 Impact Factor - TAIWANESE JOURNAL OF MATHEMATICS 03/2013; 17(1):109-131. · 0.62 Impact Factor

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