Totally umbilical CR-submanifolds of a Kaehler manifold
It was proved [see the reviewer, Geometry of CR-submanifolds (1986; Zbl 0605.53001); Theorem 2.1, p. 43] that a totally umbilical CR-submanifold M of a Kaehler manifold N is either totally geodesic or totally real, or dim \(D^{\perp}=1\). In the last case, \textit{T. Toyonari} and \textit{H. Nemoto} [TRU Math. 21, 61-66 (1985; Zbl 0578.53039)] proved that M is a Sasakian manifold. The present authors prove that in case dim \(D^{\perp}=1\) M is isometric to an ordinary sphere or it is homothetic to a Sasakian manifold.
scientific article; zbMATH DE number 3982007