Some Conformal Transformations on Finsler Warped Product Manifolds

The conformal transformation, which preserves Einstein metrics on Finsler warped product manifolds, is studied in this paper. We obtain sufficient and necessary conditions of a conformal transformation preserving Einstein metrics. In addition, we provide nontrivial examples of conformal transformations. Furthermore, we completely classify Einstein Riemannian warped product metrics and obtain the existence of a nontrivial conformal transformation that preserves Einstein metrics.

Automated summary

This paper studies the conformal transformation that preserves Einstein metrics on Finsler warped product manifolds. Sufficient and necessary conditions for a conformal transformation preserving Einstein metrics are obtained. Nontrivial examples of conformal transformations are provided. Furthermore, Einstein Riemannian warped product metrics are completely classified and the existence of a nontrivial conformal transformation preserving Einstein metrics is obtained.