The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold

DOI10.1007/s12220-022-01072-1OpenAlexW4307647696WikidataQ115229536 ScholiaQ115229536MaRDI QIDQ2091080

Abdelrahman Mohamed, Dimiter Vassilev

Publication date: 31 October 2022

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

Full work available at URL: https://arxiv.org/abs/2012.15767

zbMATH Keywords

sub-Riemannian geometrySobolev inequalityYamabe equationCR and quaternionic contact structuresLichnerowicz eigenvalue estimateObata theorem

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24) Contact manifolds (general theory) (53D10) Sub-Riemannian geometry (53C17) Analysis on CR manifolds (32V20)

Cites Work

• An Obata-type theorem in CR geometry
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold
• The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds
• Quaternionic contact Einstein manifolds
• The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven
• A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
• Einstein spaces admitting a one-parameter group of conformal transformations
• Quaternionic contact structures in dimension 7
• Conformal quaternionic contact curvature and the local sphere theorem
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
• The Yamabe problem on quaternionic contact manifolds
• The Cayley transform and uniformly bounded representations
• Embeddability for 3-dimensional Cauchy-Riemann manifolds and CR Yamabe invariants
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
• A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian
• 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
• The Lichnerowicz-Obata theorem for the Kohn Laplacian in three dimensions
• Quaternionic contact manifolds with a closed fundamental 4-form
• The first eigenvalue of a sublaplacian on a pseudohermitian manifold
• The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold
• The optimal constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group
• AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold