AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

DOI10.1017/S0017089513000256zbMath1293.53060arXiv1208.1040OpenAlexW2963540627MaRDI QIDQ5415953

Stefan Ivanov, Dimiter Vassilev

Publication date: 19 May 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1040

zbMATH Keywords

Sasakian manifoldCR manifoldTanaka-Webster connectionObata-type theorem

Mathematics Subject Classification ID

Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Other complex differential geometry (53C56) CR structures, CR operators, and generalizations (32V05) Analysis on CR manifolds (32V20)

Related Items (6)

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 Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ The first positive eigenvalue of the sub-Laplacian on CR spheres ⋮ The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold ⋮ The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries

Cites Work

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• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
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