Uniqueness of Constant Scalar Curvature Sasakian Metrics

2015/09/22 by Jin, Xishen, Zhang, Xi
#32W20 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.06522

Abstract

In this paper, we prove that the transverse Mabuchi K-energy functional is convex along the weak geodesic in the space of Sasakian metrics. As an application, we obtain the uniqueness of constant scalar curvature Sasakian metrics modulo automorphisms for the transverse holomorphic structure.

Related

• Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics
• Convexity of the K-energy and Uniqueness of Extremal metrics -- An Expository Introduction
• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• Scalar curvature and properness on Sasaki manifolds
• Geometrical pluripotential theory on Sasaki manifolds