Totally umbilical CR-submanifolds of semi-Riemannian Kähler manifolds
Let M be a totally umbilical CR-submanifold of a Kähler manifold \(\tilde M\) endowed with a semi-Riemannian metric and \(D^{\perp}\) be the totally real distribution [see the reviewer, Geometry of CR-submanifolds (1986; Zbl 0605.53001)]. The authors prove: (i) if dim \(D^{\perp}>1\), then M is a CR-product and (ii) if dim \(D^{\perp}=1\), then M has a normal contact metric structure if and only if it has parallel second fundamental form.
scientific article; zbMATH DE number 4013468