Union curvature of a vector field in a subspace

The differential equations of union curves on a hypersurfaceV _n immersed in a RiemannianV _n+1 have been obtained by Springer 1]. These results were generalized later for a subspace in a Riemannian space by Mishra 2]. The author 3] has defined the union curvature of a vector field with respect to a curve on a hypersurfaceV _n of a RiemannianV _n+1. The purpose of this paper is to consider union curvature of a vector field with respect to a curve in a subspaceV _n of a RiemannianV _m. The author is indebted to the referee for helpful suggestions.