We deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. First, we study some properties of the curvature of mixed 3-Sasakian structures. Then we prove the identity between the class of mixed 3-Sasakian structures and the class of mixed metric 3-contact structures.
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...
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