The SasakiRicci flow and compact Sasakian manifolds of positive
transverse holomorphic bisectional curvature
Weiyong He,
2011.03.30
http://arxiv.org/abs/1103.5807
We show that Perelman's Wfunctional can be generalized to SasakiRicci flow.
When the basic first Chern class is positive, we prove a uniform bound on the
scalar curvature, the diameter and a uniform $C^1$ bound for the transverse
Ricci potential along the SasakiRicci flow, which generalizes Perelman's
results KahlerRicci flow to the Sasakian setting. We also show that the
positivity of transverse of holomorphic bisectional curvature is preserved
along the flow, using the methods and the results proved by Bando and Mok in
Kahler setting. In particular, we show that the SasakiRicci flow would
converge to a SasakiRicci soliton if the initial metric has nonnegative
transverse holomorphic bisectional curvature.
