Some Hypersurfaces with Constant Mean Curvature in a Conformally Flat Riemannian Manifold

§1. T. Otsuki [1] studied the minimal hypersurface V~n of a Riemannian manifold S~(n 1) of constant curvature if the number of the distinct principal normal curvatures is two and the multiplicities of them are at least two. He proved that V~n is locally the Riemannian prodruct S~(?)×S~(?) of two Riemannian manifolds S~(?) and S~(?) of constant curvature, where ι_1 and ι_2 are these multiplicities, respectively. In the present paper S~m denotes an m-dimensional Riemannian manifold of     

The Khler-Ricci Flow on Khler Manifolds with 2-Non-negative Traceless Bisectional Curvature Operator

The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Khler-Ricci flow. The positivity of Ricci curvature is also preserved along the Khler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Khler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Khler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.