On Conformally Killing Vector Fields on a 2-Symmetric Indecomposable Lorentzian Manifold

Abstract

A natural generalization of Killing vector fields is conformally Killing vector fields, which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, conformally Killing vector fields are studied on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal factor of the conformal analogue of the Killing equation on them depends on the behavior of the Weyl tensor. In addition, in the case when the Weyl tensor is equal to zero, nontrivial examples of conformally Killing vector fields with a variable conformal factor are constructed using the Airy functions.