The main goal of this manuscript is to investigate the properties of $N(k)$-contact metric manifolds admitting a $\mathcal{Z^\ast}$-tensor. We prove the necessary conditions for which $N(k)$-contact metric manifolds endowed with a $\mathcal{Z^\ast}$-tensor are Einstein manifolds. In this sequel, we accomplish that an $N(k)$-contact metric manifold endowed with a $\mathcal{Z^\ast}$-tensor satisfying $\mathcal{Z^\ast}(\mathcal{G}_{1},\hat{\zeta})\cdot \mathcal{\overset{\star}R}=0$ is either locally isometric to the Riemannian product $E^{n+1}(0)\times S^{n}(4)$ or an Einstein manifold. We also prove the condition for which an $N(k)$-contact metric manifold endowed with a $\mathcal{Z^\ast}$-tensor is a Sasakian manifold. To validate some of our results, we construct a non-trivial example of an $N(k)$-contact metric manifold.
$N(k)$-contact metric manifold Einstein manifold Ricci soliton $\mathcal{Z}^\star$-recurrent $\mathcal{Z^\ast}$-tensor
Primary Language | English |
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Subjects | Topology |
Journal Section | Articles |
Authors | |
Early Pub Date | May 11, 2024 |
Publication Date | May 23, 2024 |
Submission Date | January 12, 2024 |
Acceptance Date | April 11, 2024 |
Published in Issue | Year 2024 Volume: 7 Issue: 2 |
Universal Journal of Mathematics and Applications
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