The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries

2014/03/11 by Fabrice Baudoin, Baudoin, Fabrice, Bumsik Kim +1
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1403.2453

openalex publication_date 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a lower bound for the first eigenvalue of the sub-Laplacian on sub-Riemannian manifolds with transverse symmetries. When the manifold is of H-type, we obtain a corresponding rigidity result: If the optimal lower bound for the first eigenvalue is reached, then the manifold is equivalent to a 1 or a 3-Sasakian sphere.

Citations

• The subelliptic heat kernels of the quaternionic Hopf fibration

Related

• An Obata-type theorem on a three-dimensional CR manifold
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion
• The Obata first eigenvalue theorems on a seven dimensional quaternionic\n contact manifold
• A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold