Biharmonic Submanifolds in Riemannian Manifold of Quasi-constant Curvature
Let Nn+pbe an(n+p)-dimensional Riemannian manifold of quasi-constant curvature,and Mnis an n-dimensional biharmonic submanifold with the parallel mean curvature of Nn+p.whenξis tangent to Mn,we obtain a Pinching theorem that the biharmonic submanifold is minimal submanifold.Then,we also get a sufficient condition that the biharmonic hypersurface is minimal hypersurface.
quasi-constant curvaturebiharmonicminmalthe parallel mean curvature
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