Biminimal hypersurfaces in a sphere

In this paper, we mainly concentrate on the biminimal hypersurfaces in a sphere. First, we obtain some rigidity theorems for biminimal hypersurfaces. Then we give a classification of non-minimal biminimal isoparametric hypersurfaces in a sphere.

► Biminimal submanifolds are critical points of a variational problem of order 4 which generalizes minimality.
► Some rigidity theorems are proved for biminimal hypersurfaces in a sphere.
► A classification of biminimal isoparametric hypersurfaces in a sphere is obtained.