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

作者：Munteanu Marian Ioan^*; Vrancken Luc

来源：Journal of Geometry and Physics, 2014, 75: 92-97.

DOI：10.1016/j.geomphys.2013.09.003

• Chen%26apos
• s inequality
• delta-invariant
• Sasakian manifold
• Contact CR-submanifold

In his book on Pseudo-Riemannian geometry, delta-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 delta(2). %26lt;br%26gt;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 delta(2) ideal. We relate this to a special class of surfaces and obtain a complete classification in arbitrary dimensions.

• 出版日期2014-1