Uniqueness of Constant Scalar Curvature Sasakian Metrics

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.

References in corpus (2)

• Uniqueness and examples of compact toric Sasaki-Einstein metrics
• Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics

Cited by in corpus (3)

• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• Scalar curvature and properness on Sasaki manifolds
• On the convergence of the Sasaki J-flow