Connessioni di Cartan su varietà CR
The Tanaka-Webster connection for almost -manifolds and Cartan geometry
We prove that a CR-integrable almost -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...
A Frankel type theorem for CR submanifolds of Sasakian manifolds
We prove a Frankel type theorem for submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about submanifolds of Sasakian space forms.
Three-dimensional slant submanifolds of -contact manifolds.
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