If we consider strongly-pseudo convex CR manifolds with integrable CR structure, the transformation formula of the pseudo-Hermitian scalar curvatures satisfies a very special non-linear sub-elliptic PDE, which is called the CR Yamabe equation. In 1995, R. Schoen made use of this equation for the characterization of the Heisenberg group under the non-proper action of CR automorphism group.
In contrast with integrable case, the transformation formula of the pseudo-Hermitian scalar curvatures is much more complecated than the CR Yamabe equation, if the CR structure is not integrable and this complexity makes it difficult to follow the analysis of integrable case.
In this talk, I will introduce a sub-class of contact sub-Riemannian manifolds for which sub-conformal transformation formula of a twisted sub-Riemannian scalar curvature becomes the sub-conformal Yamabe equation. Using the sub-conformal Yamabe equation, we will also discuss about the characterization 5 and 7-dimenisional non-integrable strongly pseudo-convex almost CR manifolds under the non-proper action of CR automorphisms by Schoen's argument.
Seminar
Home > Activities > Basic Research > Seminar
Title 