拟常曲率黎曼流形中的2-调和子流形

Biharmonic Submanifolds in Riemannian Manifold of Quasi-constant Curvature

该文讨论了拟常曲率黎曼流形Nn+p中具有平行平均曲率的2-调和子流形Mn,在ξ∈Γ(TM)时,得到这类子流形是极小子流形的一个拼挤定理.对2-调和超曲面的情形,也得到了其为极小超曲面的一个充分条件.

Let Nn+p be 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.