Minimal contact CR submanifolds in S2n+1 satisfying the δ(2)-Chen equality

In his book on Pseudo-Riemannian geometry, δ -invariants and applications, B.Y. Chen introduced a sequence of curvature invariants. Each of these invariants is used to obtain a lower bound for the length of the mean curvature vector for an immersion in a real space form. A submanifold is called an ideal submanifold, for that curvature invariant, if and only if it realizes equality at every point. The first such introduced invariant is called δ ( 2 ) . On the other hand, a well known notion for submanifolds of Sasakian space forms, is the notion of a contact CR-submanifold. In this paper we combine both notions and start the study of minimal contact CR-submanifolds which are δ ( 2 ) ideal. We relate this to a special class of surfaces and obtain a complete classification in arbitrary dimensions.