Turkish Journal of Mathematics
Abstract
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, $EWS(g,w,\pi,\mu)$.
DOI
10.3906/mat-1803-121
Keywords
Weyl manifold, semisymmetric connection, recurrent-metric connection, generalized Bianchi identities, sectional curvature
First Page
224
Last Page
240
Recommended Citation
ÖZDEMİR, F, & TÜRKOĞLU, M. D (2019). Sectional curvatures on Weyl manifolds with a special metric connection. Turkish Journal of Mathematics 43 (1): 224-240. https://doi.org/10.3906/mat-1803-121
