Nonnegativity of CR Paneitz operator and its application to the CR Obata's theorem

DOI10.1007/s12220-008-9060-9zbMath1205.32026OpenAlexW2092958551MaRDI QIDQ836229

Shu-Cheng Chang, Hung-Lin Chiu

Publication date: 31 August 2009

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: http://ntur.lib.ntu.edu.tw/bitstream/246246/183994/1/02.pdf

zbMATH Keywords

eigenvaluespseudo-Hermitian structuresub-LaplacianTanaka-Webster curvatureCR-invariant differential operatorLichnerowicz-Obata theoremWebster metric

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Other complex differential geometry (53C56) CR structures, CR operators, and generalizations (32V05) Analysis on CR manifolds (32V20)

Related Items (24)

Dirichlet and Neumann eigenvalue problems on CR manifolds ⋮ An optimal gap theorem in a complete strictly pseudoconvex CR \((2n+1)\)-manifold ⋮ The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven ⋮ On the Sharp Dimension Estimate of CR Holomorphic Functions in Sasakian Manifolds ⋮ A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold ⋮ On the three-circle theorem and its applications in Sasakian manifolds ⋮ Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian manifolds ⋮ The CR almost Schur lemma and Lee conjecture ⋮ An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion ⋮ Uniformization of spherical \( CR\) 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 ⋮ ON HARMONIC AND PSEUDOHARMONIC MAPS FROM PSEUDO-HERMITIAN MANIFOLDS ⋮ A lower bound on the spectrum of the Sublaplacian ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ A positive mass theorem in three dimensional Cauchy-Riemann geometry ⋮ Uniqueness results on CR manifolds ⋮ 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 ⋮ On CR volume growth estimate in a complete pseudohermitian 3-manifold ⋮ Complete Pseudohermitian manifolds with positive spectrum ⋮ On the CR Poincaré-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds ⋮ The diameter estimate and its application to CR Obata’s Theorem on closed pseudohermitian $(2n+1)$-manifolds ⋮ The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries

Cites Work

• Unnamed Item
• On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold
• Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains
• The sharp lower bound for the first positive eigenvalue of the sublaplacian on a pseudohermitian 3-manifold
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• The first eigenvalue of a sublaplacian on a pseudohermitian manifold
• The Fefferman Metric and Pseudohermitian Invariants
• Psuedo-Einstein Structures on CR Manifolds
• The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold
• A fourth order curvature flow on a CR 3-manifold
• Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces

This page was built for publication: Nonnegativity of CR Paneitz operator and its application to the CR Obata's theorem