The Wu-Yau theorem on Sasakian manifolds

2021/09/12 by Chen, Yong
#53C25 #53C56 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05414

Abstract

In this note, We proved that a compact Sasakian manifold ( M, ξ, η, Φ , g ) with negative transverse holomorphic sectional curvature must have has a Sasakian structure ( ξ, η , Φ , g ) with negative transverse Ricci curvature. Similarly, a compact Sasakian manifold with non-positive transverse holomorphic sectional curvature, then the negative first basic Chern class 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.

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