Ricci curvature lower bounds on Sasakian manifolds

Abstract

Measure contraction property is a synthetic Ricci curvature lower bound for metric measure spaces. We consider Sasakian manifolds with non-negative Tanaka-Webster Ricci curvature equipped with the metric measure space structure defined by the sub-Riemannian metric and the Popp measure. We show that these spaces satisfy the measure contraction property $MCP(0,N)$ for some positive integer $N$. We also show that the same result holds when the Sasakian manifold is equipped with a family of Riemannian metrics extending the sub-Riemannian one.

30 pages

References in corpus (3)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• The splitting theorem in non-smooth context
• On measure contraction property without Ricci curvature lower bound

Cited by in corpus (1)

• Volume Rigidity of Principal Circle Bundles over the Complex Projective Space