$*$-Weyl curvature tensor within the framework on Sasakian manifold admitting Zamkovoy connection | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Article 9, Volume 13, Issue 2, 2025, Pages 1-9 PDF (212.16 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.345588.1301 | ||
| Authors | ||
| Pavithra R.C.* 1; H. G. Nagaraja2 | ||
| 1Department of Mathematics, Bangalore University Bengaluru | ||
| 2Department of Mathematics, Bangalore University Bengaluru | ||
| Abstract | ||
| In this paper, we investigate $*$-Weyl curvature tensor of Sasakian manifold admitting Zamkovoy connection. If a sasakian manifold $M$ is Ricci flat with respect to the Zamkovoy connection then $M$ is an $\eta$-Einstein manifold. We study $*$-Weyl flat Sasakian manifold $M$ admitting Zamkovoy connection $\overline{\nabla}$ is an $\eta$-Einstein manifold. as well as $\xi$-$*$-Weyl flat Sasakian manifolds admitting Zamkovoy connection is an $\eta$-Einstein manifold, then its scalar curvature is constant. Additionally, we prove $\phi$-$*$-Weyl flat Sasakian manifolds admitting Zamkovoy connection then manifold is an $\eta$-Einstein manifold. Also $\xi$-$*$-Weyl flat with respect to Zamkovoy connection if and only if it is with respect Levi-Civita connection, provided that vector fields are horizantal vector fields. Moreover, We also prove that Sasakian manifolds satisfying $\overline{W}^{*}(\xi,U)\circ\overline{R}=0$, where $\overline{W}^{*}$ and $\overline{R}$ are $*$-Weyl curvature tensor and Riemannian curvature tensor with respect to Zamkovoy connection, meet specific conditions. Finally we conclude with an example for three-dimensional Sasakian manifolds. | ||
| Keywords | ||
| Sasakian manifold; $*$-Weyl curvature tensor; Zamkovoy connection | ||
|
Statistics Article View: 65 PDF Download: 79 |
||
