Biharmonic submanifolds in a Riemannian manifold with non-positive curvature

Details Biharmonic submanifolds in a Riemannian manifold with non-positive curvature Biharmonic submanifolds in a Riemannian manifold with non-positive curvature

2012-01-31

arxiv.org/abs/1201.6455v1

Mathematics

Differential Geometry

Scientific paper

We show that for an isometric immersion of a complete Riemannian manifold
into a Riemannian manifold with non-positive curvature, the norm of the mean
curvature vector field is square integrable, then it is minimal. This is a
partial affirmative answer of the B. Y. Chen's conjecture.

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