On Permanent vector-varieties in n-dimensions

Abstract

J. L. SYNGS [1951] has recently given a generalization to the Euclidean space of n dimensions of ZORAWSKI'S condition for the permanence of vector-lines in a moving fluid. The purpose of this note is to consider the more general case in which instead of vector-lines we have varieties of dimension r >= 1 defined by certain vector fields. We obtain a necessary and sufficient condition for the permanence of these r-dimensional vector-varieties in a moving fluid. The method we follow is analogous to that of SYNGE