The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature

Details The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature

2011-03-30

arxiv.org/abs/1103.5807v1

Mathematics

Differential Geometry

Scientific paper

We show that Perelman's W-functional can be generalized to Sasaki-Ricci 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 Sasaki-Ricci flow, which generalizes Perelman's results Kahler-Ricci 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 Sasaki-Ricci flow would converge to a Sasaki-Ricci soliton if the initial metric has nonnegative transverse holomorphic bisectional curvature.

Affiliated with

Also associated with

No associations

Rating

The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-567251