On quasirecurrent manifolds

We introduce a type of Riemannian manifolds (namely, quasirecurrent manifold) and study its several geometric properties. Among others, we prove that the scalar curvature of such a manifold is constant, and that the manifold is Einstein under certain condition. In addition, we deal with a quasirecurrent product manifold. Finally, we ensure the existence of quasirecurrent manifold by a proper example.