Abstract
In this article, we show that the presence of a torqued vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian manifolds of constant curvature. More precisely, we show that there is no torqued vector field on n-sphere S-n(c). A nontrivial example of torqued vector field is constructed on an open subset of the Euclidean space E-n whose torqued function and torqued form are nowhere zero. It is shown that owing to topology of the Euclidean space E-n, this type of torqued vector fields could not be extended globally to E-n. Finally, we find a necessary and sufficient condition for a torqued vector field on a compact Riemannian manifold to be a concircular vector field.