F-Willmore submanifold in space forms

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.

Keywords

Mean curvature / Willmore submanifold / Simons’ type integral inequality

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