The Webster scalar curvature revisited: The case of the three dimensional \(C R\) sphere

DOI10.1007/s00526-010-0382-7zbMath1222.58008OpenAlexW2113748401MaRDI QIDQ635769

Eljazi Salem, Najoua Gamara

Publication date: 23 August 2011

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-010-0382-7

zbMATH Keywords

conformal LaplacianMorse lemmaWebster scalar curvaturepseudo-gradient

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Critical points and critical submanifolds in differential topology (57R70)

Related Items (12)

Prescribed Webster scalar curvature on \(S^{2n+1}\) in the presence of reflection or rotation symmetry ⋮ Existence results for the fractional Q-curvature problem on three dimensional CR sphere ⋮ The impact of the flatness condition on the prescribed webster scalar curvature ⋮ Methods of the theory of critical points at infinity on Cauchy Riemann manifolds ⋮ CR Nirenberg problem and zero Wester scalar curvature ⋮ Perturbation of the CR fractional Yamabe problem ⋮ The Webster scalar curvature flow on CR sphere. I ⋮ The Webster scalar curvature flow on CR sphere. II ⋮ Optimal control in prescribing Webster scalar curvatures on 3-dimensional pseudo Hermitian manifolds ⋮ The {\(\beta\)}-flatness condition in CR spheres ⋮ RESULTS RELATED TO PRESCRIBING PSEUDO-HERMITIAN SCALAR CURVATURE ⋮ Prescribed Webster scalar curvatures on compact pseudo-Hermitian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• CR Yamabe conjecture -- the conformally flat case.
• Prescribing Gaussian curvature on \(S^ 2\)
• The scalar-curvature problem on the standard three-dimensional sphere
• Prescribing Gaussian curvature on S 2
• Conformal deformations of metric on \({\mathcal S}\) 2
• The Yamabe problem on CR manifolds
• Intrinsic CR normal coordinates and the CR Yamabe problem
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
• A perturbation result for the Webster scalar curvature problem on the CR sphere.
• On the prescribed scalar curvature problem on 4-manifolds
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension
• Differential geometry and analysis on CR manifolds
• The Webster scalar curvature problem on the three dimensional CR manifolds
• Some existence results for the Webster scalar curvature problem in presence of symmetry
• The Prescribed Scalar Curvature on a 3 - Dimensional CR Manifold
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Scalar Curvatures on S 2
• ON NIRENBERG'S PROBLEM
• The CR Yamabe conjecture. The case \(n=1\)

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