SOME IMPORTANT CHARACTERIZATION OF W9-CURVATURE TENSOR IN LORENTZIAN α-SASAKIAN MANIFOLD

다국어 초록 (Multilingual Abstract)

The objective of this paper is to explore some curvature properties of $\mathcal{W}_9$-curvature tensor in Lorentzian $\alpha$-Sasakian manifold $(\mathcal M_\alpha)$. Initially, we establish certain vanishing properties of $\mathcal{W}_9$-curvature tensor in $\mathcal M_\alpha$ and arrive at a range of valuable insights. Subsequently, we describe $\varphi$-$\mathcal{W}_9$-semi-symmetric condition in $\mathcal M_\alpha$. Further, we explore $\mathcal M_\alpha$ satisfying the condition $\mathcal{Q}\cdot \mathcal{W}_9=0$. Again, we discuss $\mathcal{W}_9$ Ricci pseudo-symmetric condition on $\mathcal M_\alpha$. Next, we deal with $\mathcal M_\alpha$ satisfying $\mathcal{W}_9\cdot \mathcal{R}=0$ condition. Later, we formulate $\mathcal{V}^\flat$-Ricci soliton and conformal $\mathcal{V}^\flat$-Ricci soliton. At last, we present an example of $5$-dimensional $\mathcal M_\alpha$ which verifies our results.