3 citations · 6 across the 6 of their papers we have counts for
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Curvatures and hyperbolic flows for natural mechanical systems in Finsler geometry
Chengbo Li
We consider a natural mechanical system on a Finsler manifold and study its \emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi curves}) along the extremals…
Bishop and Laplacian comparison theorems on Sasakian manifolds
Paul W. Y. Lee, Chengbo Li
We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for a natural sub-Riemannian structure defined on Sasakian manifolds. This generalizes the earlier wo…
Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds
Paul W. Y. Lee, Chengbo Li, Igor Zelenko
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 giv…
A note on sub-Riemannian structures associated with complex Hopf fibrations
Chengbo Li, Huaying Zhan
Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian stru…
A note on hyperbolic flows in sub-Riemannian Structures
Chengbo Li
The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the n…
Jacobi Equations and Comparison Theorems for Corank 1 sub-Riemannian Structures with Symmetries
Chengbo Li, Igor Zelenko
The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about th…