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arXiv · 1403.2453

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

Fabrice Baudoin·Bumsik Kim
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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.

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Fabrice Baudoin, Bumsik Kim. 2014-07-30. The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries. https://arxiv.org/abs/1403.2453

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