In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
ÖZDEMİR, FATMA and TÜRKOĞLU, MUSTAFA DENİZ
"Sectional curvatures on Weyl manifolds with a special metric connection,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/18