  We propose a geometric ansatz, a restriction on Euclidean / Minkowski
distance in the embedding space being propotional to distance in the embedded
space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i
u^k = 0, u_i u^i = 1 $). It turns out that these spacetimes can represent
global monopoles and textures. Thus the ansatz is a prescription to generate
zero mass spacetimes that could describe topological defects, global monopoles
and textures.
