A link between torse-forming vector fields and rotational hypersurfaces

Author:

Chen Bang-Yen1,Verstraelen Leopold2

Affiliation:

1. Department of Mathematics, Michigan State University, East Lansing, Michigan 48824–1027, USA

2. Departement Wiskunde, KU Leuven, Celestijnenlaan 200 B, BE-3001 Leuven, Belgium

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

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