Torse-forming vector fields in \(T\)-semisymmetric Riemannian spaces (Q2733942)

A Riemannian space \(V_n\) is called \(T\)-semisymmetric, where \(T\) is a tensor field on \(V_n\), if the curvature tensor field \(R\) satisfies the condition \(R(X,Y)\circ T=0\), for arbitrary vector fields \(X,Y\). A vector field \(\xi\) on \(V_n\) is called torse-forming if there are a function \(\rho\) and a 1-form \(\alpha\) so that \(\nabla_X\xi =\rho X+\alpha (X)\xi\). In this paper the authors establish some properties for torse-forming vectors fields in a \(T\)-semisymmetric Riemannian space, where \(T\) is 1-form, a 2-covariant tensor field or the Ricci tensor field of \(V_n\).NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].