David, Liana Weyl connections and curvature properties of CR manifolds. (English) Zbl 1054.32022 Ann. Global Anal. Geom. 26, No. 1, 59-72 (2004). 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 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. Reviewer: Mauro Nacinovich (Roma) Cited in 1 ReviewCited in 6 Documents MSC: 32V99 CR manifolds 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:Tanaka and Weyl connections; strictly pseudoconvex CR manifolds; hypersurface type Citations:Zbl 0331.53025 PDFBibTeX XMLCite \textit{L. David}, Ann. Global Anal. Geom. 26, No. 1, 59--72 (2004; Zbl 1054.32022) Full Text: DOI