Homotopy connectedness theorems for submanifolds of Sasakian manifolds

摘要

The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and (κ,ε)-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak (ε-)asymptotic index. As a corollary, the Frankel type theorem is proved.