On some conformally einstein manifolds of dimension four

Abstract

We study an important family of four-dimensional pseudo-Riemannian manifolds, i.e. generalized symmetric spaces, in terms of conformal geometry. Generalized symmetric spaces were introduced by geometers as an extension of symmetric spaces, and a detailed classification of them was presented in low dimensions, i.e. up to four dimensions. Today, many studies have been done on this family of (pseudo)-Riemannian manifolds. Due to its relationship with the inherent geometry of space, conformal geometry has always been in focus of researchers. Therefore, many geometric features can be studied, which are established in the conformal class of space. One of these properties that is also important in physics is the property of being Einstein. As a result of this study, a general classification of conformally Einstein metrics in generalized symmetric spaces of dimension four is presented.

Keywords

• generalized symmetric spaces
• einstein metric
• conformal geometry