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The Lichnerowicz–Obata Theorem on Sub-Riemannian Manifolds with Transverse Symmetries

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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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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, USA

    Fabrice Baudoin & Bumsik Kim

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  1. Fabrice Baudoin
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  2. Bumsik Kim
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Correspondence to Fabrice Baudoin.

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Communicated by Der-Chen Edward Chang.

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Baudoin, F., Kim, B. The Lichnerowicz–Obata Theorem on Sub-Riemannian Manifolds with Transverse Symmetries. J Geom Anal 26, 156–170 (2016). https://doi.org/10.1007/s12220-014-9542-x

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  • DOI: https://doi.org/10.1007/s12220-014-9542-x

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