Sasaki Metric on the Tangent Bundle of a Weyl Manifold

Cornelia-Livia Bejan, İlhan Gül

Let $(M,[g])$ be a Weyl manifold of dimension $m>2$. By using the Sasaki metric $G$ induced by $g$, we construct a Weyl structure on $TM$. Then we prove that it is never Einstein--Weyl unless $(M,g)$ is flat. The main theorem here extends to the Weyl context a result of Musso and Tricerri.