Weyl connections and curvature properties of CR manifolds
The author considers strictly pseudoconvex CR manifolds \(M\) of the hypersurface type. Denoting by \(H\) the analytic tangent bundle of \(M\), she defines a Weyl connection on \(M\) as a connection \(D\) on the line bundle \(TM/H\). She proves that to such a \(D\) one can associate in a unique way an affine connection \(\nabla\) on \(TM\), yielding for an exact \(D\) the one defined by \textit{N.Tanaka} in [A differential geometric study on strongly pseudo-convex manifolds (1975; Zbl 0331.53025)]. This construction simplifies the definition of the Chern-Moser tensor on \(M\) and makes clearer its connection with the Bochner tensor for a Sasakian CR manifold.
scientific article; zbMATH DE number 2093689