On invariant submanifolds of \(\mathcal C\)- and \(\mathcal S\)-manifolds
\(\mathcal S\)- and \(\mathcal C\)-structures are interesting cases of \(f\)-structures [see \textit{D. E. Blair}, J. Differ. Geom. 4, 155-167 (1970; Zbl 0202.20903)]. First the properties of the second fundamental form and the Weingarten operator are studied, and some observations on the curvature tensors are given. Then it is proved that the second fundamental form of a submanifold of an \(\mathcal S\)-manifold is parallel if and only if it is totally geodesic. By a counterexample it is shown that this is not true for \(\mathcal C\)-manifolds.
scientific article; zbMATH DE number 1446810