2013/04/09 by Paul W. Y. Lee, Chengbo Li, Lee, Paul W. Y. +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #53A55 #53C17 #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53A55 #msc:53C17
paper · pdf · doi:10.48550/arxiv.1304.2658
25 pages
openalex publication_date 2013/04/09 · arxiv created 2014/11/09 · arxiv updated 2014/11/11 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
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 \citeAgLe1 for the three dimensional case and in \citeJu 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 \citeLiZe1, LiZe2. 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.