A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold

zbMath1474.53202arXiv1404.4377MaRDI QIDQ4993809

Alexander Petkov

Publication date: 16 June 2021

Full work available at URL: https://arxiv.org/abs/1404.4377

zbMATH Keywords

first eigenvaluesub-Laplacianquaternionic contact structuresLichnerowicz inequality3-Sasakian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Sub-Riemannian geometry (53C17)

Cites Work

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• An Obata-type theorem in CR geometry
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold
• Quaternionic contact Einstein manifolds
• The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven
• On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold
• Nonnegativity of CR Paneitz operator and its application to the CR Obata's theorem
• Conformal paracontact curvature and the local flatness theorem
• Quaternionic contact structures in dimension 7
• Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains
• On the estimate of the first eigenvalue of a sub-Laplacian on a pseudo-Hermitian 3-manifold
• Conformal quaternionic contact curvature and the local sphere theorem
• The entropy formulas for the CR heat equation and their applications on pseudohermitian \((2n+1)\)-manifolds
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
• Pluriharmonic boundary values
• Real hypersurfaces in complex manifolds
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
• The Lichnerowicz theorem on CR manifolds
• 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 sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven
• Quaternionic contact manifolds with a closed fundamental 4-form
• The dirichlet problem for the bezgman laplacian. II
• The first eigenvalue of a sublaplacian on a pseudohermitian manifold
• Psuedo-Einstein Structures on CR Manifolds
• The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold
• Yang-Mills fields on quaternionic spaces
• A fourth order curvature flow on a CR 3-manifold