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
Birincil Dil | İngilizce |
---|---|
Konular | Topoloji |
Bölüm | Makaleler |
Yazarlar | |
Erken Görünüm Tarihi | 11 Mayıs 2024 |
Yayımlanma Tarihi | 23 Mayıs 2024 |
Gönderilme Tarihi | 12 Ocak 2024 |
Kabul Tarihi | 11 Nisan 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 7 Sayı: 2 |
Universal Journal of Mathematics and Applications
The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.