On biharmonic submanifolds in non-positively curved manifolds

摘要

In the biharmonic submanifolds theory there is a generalized Chen's conjecture which states that biharmonic submanifolds in a Riemannian manifold with non-positive sectional curvature must be minimal. This conjecture turned out false by a counter example of Y.L. Ou and L Tang in Ou and Tang (2012). However it remains interesting to find out sufficient conditions which guarantee this conjecture to be true. In this note we prove that: