Source: wikibot/homothetic-vector-field
= Homothetic vector field
{wiki=Homothetic_vector_field}
A homothetic vector field is a type of vector field in differential geometry and the study of Riemannian manifolds that encodes self-similarity characteristics of the manifold. More precisely, a vector field \\( V \\) on a Riemannian manifold \\( (M, g) \\) is said to be homothetic if it generates homotheties of the metric \\( g \\).