Sasaki manifolds with positive transverse orthogonal bisectional curvature

Abstract

Abstract In this short note we show the following result: Let (M2n+1, g) with n ≥ 2 be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then π1(M) is finite, and the universal cover of (M2n+1, g) is isomorphic to a simple metric on a weighted Sasaki sphere.We also get some results in the case of nonnegative transverse orthogonal bisectional curvature under some additional conditions. This extends recent work of He and Sun. The proof uses the Sasaki-Ricci flow.