Abstract

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold <TEX>$M_q$</TEX> of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in <TEX>$M_q$</TEX>, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in <TEX>$M_q$</TEX>.