Ricci curvature lower bounds on Sasakian manifolds

2015/11/30 by Paul W. Y. Lee, Lee, Paul W. Y.
Mathematics · #31E05 #53C17 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:31E05 #msc:53C17

paper · pdf · doi:10.48550/arxiv.1511.09381

30 pages

arxiv created 2015/12/26 · arxiv updated 2015/12/29

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.

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