The Wu–Yau theorem on Sasakian manifolds

Abstract

In this paper, we proved that a compact Sasakian manifold [Formula: see text] with negative transverse holomorphic sectional curvature must have a Sasakian structure [Formula: see text] with negative transverse Ricci curvature. Similarly, a compact Sasakian manifold with nonpositive transverse holomorphic sectional curvature, then the negative first basic Chern class [Formula: see text] is transverse nef and we have the Miyaoka–Yau-type inequality. When transverse holomorphic sectional curvature is quasi-negative, we obtain a Chern number inequality.