In this paper, it is proved that if, at each point of a Weyl manifold, the sectional curvature is independent of the plane chosen, then the Weyl manifold is locally conformal to an Einstein manifold and that the scalar curvature of the Weyl manifold is prolonged covariant constant.
Özdeğer Abdülkadir. "On sectional curvatures of a Weyl manifold." Proc. Japan Acad. Ser. A Math. Sci. 82 (8) 123 - 125, November 2006. https://doi.org/10.3792/pjaa.82.123