Geometric vector fields on Riemannian manifolds

Among the vector fields defined on a Riemannian manifold (M, g) there are special ones whose properties are related with the underlying geometry of the space that, generically, are called geometric vector fields. In this context, this project is focused on the study of the properties and behavior of the so-called 2-Killing vector fields on Riemannian manifolds, and elucidate their relation with other well-known geometric vector fields that appear in the literature.