A note on some properties of 4-dimensional walker metrics

Abstract

This paper is devoted to examine a special case of Walker metric on a 4-dimensional manifold, and some of its curvature properties are studied, e.g., conditions for a Walker metric to be Einstein or locally conformally flat. Finally, a necessary and sufficient condition for a function c(x, y, z, t) of Walker metric of 4-dimensional manifold to have vector field X on M to be a Killing vector field, is constructed.