Minimal contact CR submanifolds in S2n+1 satisfying the delta(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. © 2013 Elsevier B.V.

Publication year:2014

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Authors:International

Authors from:Higher Education