• Corpus ID: 214802512

Sub-Riemannian Ricci curvature via generalized Gamma $z$ calculus

@article{Feng2020SubRiemannianRC,
  title={Sub-Riemannian Ricci curvature via generalized Gamma \$z\$ calculus},
  author={Qi Feng and Wuchen Li},
  journal={arXiv: Differential Geometry},
  year={2020}
}
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group ($\textbf{SE}(2)$), and Martinet sub-Riemannian structure with arbitrary weighted volumes, in which we establish analytical bounds for sub-Riemannian curvature dimension bounds and log-Sobolev inequalities. Our derivation of Ricci curvature is based on generalized Gamma $z$ calculus and $z$--Bochner's formula, where $z$ stands for extra directions… 
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