On some special symmetries of a biwarped product-type 3-manifold

Abstract

We investigate special Killing vector fields on 3-dimensional Riemannian manifolds of biwarped product-type. Starting from a diagonal metric on $\mathbb R^3$ determined by two nontrivial warping functions and a constant scaling factor, we derive the system of equations characterizing Killing fields and provide a description of their structure. Families of solutions are obtained, depending on the expressions and on the relations between the warping functions, including explicit examples of both warped and biwarped product cases. These results continue recent work on symmetries of manifolds with diagonal metrics.