On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold

DOI10.1007/s00208-009-0339-3zbMath1182.32012OpenAlexW2024074356MaRDI QIDQ834773

Hung-Lin Chiu, Shu-Cheng Chang

Publication date: 27 August 2009

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: http://ntur.lib.ntu.edu.tw/bitstream/246246/184005/1/04.pdf

zbMATH Keywords

Obata's theorempseudohermitian 3-manifolds

Mathematics Subject Classification ID

Other complex differential geometry (53C56) CR structures, CR operators, and generalizations (32V05) Analysis on CR manifolds (32V20)

Related Items (22)

Nonnegativity of CR Paneitz operator and its application to the CR Obata's theorem ⋮ The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven ⋮ Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold ⋮ A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold ⋮ CR sub-Laplacian comparison and Liouville-type theorem in a complete noncompact Sasakian manifold ⋮ An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion ⋮ \(C_0\)-positivity and a classification of closed three-dimensional CR torsion solitons ⋮ Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds ⋮ The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold ⋮ The Bochner-type formula and the first eigenvalue of the sub-Laplacian on a contact Riemannian manifold ⋮ Differential Harnack estimates for time-dependent heat equations with potentials in a closed spherical CR 3-manifold ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ On three-dimensional CR Yamabe solitons ⋮ The sharp upper bounds for the first positive eigenvalue of the Kohn-Laplacian on compact strictly pseudoconvex hypersurfaces ⋮ The first positive eigenvalue of the sub-Laplacian on CR spheres ⋮ On the CR–Obata theorem and some extremal problems associated to pseudoscalar curvature on the real ellipsoids in $\mathbb{C}^{n+1}$ ⋮ AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD ⋮ Complete Pseudohermitian manifolds with positive spectrum ⋮ Inequalities for eigenvalues of the sub-Laplacian on strictly pseudoconvex CR manifolds ⋮ CR gradient estimate for the positive eigenfunction of Witten sub-Laplacian ⋮ The diameter estimate and its application to CR Obata’s Theorem on closed pseudohermitian $(2n+1)$-manifolds ⋮ Subgradient estimates for the equation \(\Delta_bu+cu^{-\alpha}=0\) on complete pseudohermitian manifolds

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• A fourth order curvature flow on a CR 3-manifold
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