Some properties of biconcircular gradient vector fields

摘要

We consider a Riemannian manifold carrying a biconcircular gradient vector field X, having as generative a closed torse forming U. The existence of such an X is determined by an exterior differential system in involution depending on two arbitrary functions of one argument. The Riemannian manifold is foliated by Einstein surfaces tangent to X and U. Properties of the biconcircular vector field X  are investigated.