The generalized Frankel conjecture in Sasaki geometry
Differential Geometry
2012-09-19 v1
Abstract
We prove some structure results for \emph{transverse reducible} Sasaki manifolds. In particular, we show Sasaki manifolds with positive Ricci curvature is transversely irreducible, and so there is no join (product) construction for irregular Sasaki-Einstein manifolds, as opposed to the quasi-regular case done by Wang-Ziller and Boyer-Galicki. As an application, we classify compact Sasaki manifolds with non-negative transverse bisectional curvature, which can be viewed as the generalized Frankel conjecture (N. Mok's theorem) in Sasaki geometry.
Cite
@article{arxiv.1209.4026,
title = {The generalized Frankel conjecture in Sasaki geometry},
author = {Weiyong He and Song Sun},
journal= {arXiv preprint arXiv:1209.4026},
year = {2012}
}