A link between torse-forming vector fields and rotational hypersurfaces

Abstract

Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340–346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More precisely, our main result states that, for a hypersurface [Formula: see text] of [Formula: see text] with [Formula: see text], the tangential component [Formula: see text] of the position vector field of [Formula: see text] is a proper torse-forming vector field on [Formula: see text] if and only if [Formula: see text] is contained in a rotational hypersurface whose axis of rotation contains the origin.