On totally umbilical submanifolds in a \(\widetilde{C}\) recurrent space (Q2732375)

Let \((N,g)\) be a Riemannian manifold. The authors define a 4-tensor \(C\) by using curvature tensor, Ricci tensor, metric \(g\) and three constants. \((N,g)\) is called a \(C\)-recurrent space, if there exists some 1-form \(\omega\) such that \(\nabla_XC =\omega(X)\) for all vector fields \(X\), where \(\nabla\) is the Levi-Civita connection. In this paper some results concerning totally umbilical submanifolds in a \(C\)-recurrent space are obtained.