Pseudo-conformal invariants of type (1,3) of CR manifolds
Let (M,\(\eta\),g) be a real \((2n+1)\)-dimensional contact Riemannian manifold with a contact form \(\eta\) and a Riemannian metric g associated to \(\eta\). Denote by D the contact distribution on M and by \(D^*\) the dual of D. It is well known that D admits an almost complex structure J and thus M has a pseudo-Hermitian structure (\(\eta\),J). The author calls \(B\in \Gamma (D\otimes D^{*3})\) a pseudo-conformal invariant of type (1,3), if B of (M,\(\eta\),J) is the same with \(\bar B\) of (M,\(\eta\),J) for the change \(\eta\to {\bar \eta}=\sigma \eta\), where \(\sigma\) is a smooth function. The author proves that (M,\(\eta\),g) admits such an invariant which depends on the linear connection on M. In case the CR-structure associated with the contact Riemannian structure is integrable, this invariant is just the Chern-Moser invariant.
scientific article; zbMATH DE number 4201072