Minimal contact CR submanifolds in [formula omitted] satisfying the [formula omitted]-Chen equality

Abstract

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.