Three-dimensional CR-submanifolds in the nearly Kaehler six-sphere satisfying B. Y. Chen's basic equality. (Q2711245)

\textit{B.-Y. Chen} [Arch. Math. 60, 568--578 (1993; Zbl 0811.53060)] proves the inequality for an arbitrary \(n\)-dimensional Riemannian submanifold \(M\) in a real space form of constant curvature \(c\): NEWLINE\[NEWLINE\delta\leq\frac{n^2(n-2)}{2(n-1)}\| H\|^2+\frac{1}{2}(n+1)(n-2)c,NEWLINE\]NEWLINE where \(\delta\) is a function on \(M\) defined by \(\delta=\) the scalar curvature \(-\) the infimum of the sectional curvature at each point, and \(H\) denotes the mean curvature vector.NEWLINENEWLINE The author studies \(3\)-dimensional CR-submanifolds in the nearly Kähler \(6\)-sphere which satisfy the equality in the Chen's inequality.