Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds
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Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped with a natural sub-Riemannian distance to satisfy these properties. Moreover, the sufficient conditions are defined by the Tanaka-Webster curvature. This generalizes the earlier work in  for the three dimensional case and in  for the Heisenberg group. To obtain our results we use the intrinsic Jacobi equations along sub-Riemannian extremals, coming from the theory of canonical moving frames for curves in Lagrangian Grassmannians [24, 25]. The crucial new tool here is a certain decoupling of the corresponding matrix Riccati equation. It is also worth pointing out that our method leads to exact formulas for the measure contraction in the case of the corresponding homogeneous models in the considered class of sub-Riemannian structures.
Discrete and Continuous Dynamical Systems
author list (cited authors)
Lee, P., Li, C., & Zelenko, I.
complete list of authors
Lee, Paul WY||Li, Chengbo||Zelenko, Igor