Öz
The classification of almost contact $B-$metric manifolds is considered. It is shown that $\mathcal{D}-$homothetic deformation of these manifolds in the class $\mathcal{F}_{i}$ $\left( i=0,1,4,5\right) $ remains in the same the class $\mathcal{F}_{i}$. We study almost contact $B-$metric structure on $5-$dimensional nilpotent Lie algebras. The class of the left invariant almost contact $B-$metric structures on corresponding Lie groups is investigated. Finally, we determine the class of $5-$dimensional nilpotent Lie algebras with almost contact $B-$metric structure.
Anahtar Kelimeler
5-dimensional nilpotent lie algebra almost contact $B-$metric manifold fundamental tensor
Kaynakça
- [1] Bulut, Ş.: D-homothetic deformation on almost contact B-metric manifolds. J. of Geo. 110(23), (2019).
- [2] Chinea, D., Gonzalez, C.: A classification of almost contact metric manifolds. An.Sti.Univ."Al.I.Cuza"Iasi. 30, 75-79 (1984).
- [3] Dixmier, J.: Sur les representations unitaires des groupes de Lie nilpotentes III. Canadian Journal of Mathematics. 10, 321-348 (1958).
- [4] Ganchev, G., Borisov, A.: Note on almost contact manifolds with Norden metric. Compt. Rend. Acad. Bulg. Sci. 39, 31-34 (1986).
- [5] Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric. Mathematica Balkanica. 7, 261-276 (1993).
- [6] Manev, M.: Curvature properties on some classes of almost contact manifolds with B-metric. Compt. Rend. Acad. Bulg. Sci. 65 (4), 283-290 (2012).
- [7] Manev, H.: On the structure tensors of almost of contact B-metric Manifolds. Filomat. 29(3), 427-436 (2015).
- [8] Morimoto, A.: On normal almost contact structures. J. Math. Soc. Japan. 15, 420-436 (1963).
- [9] Özdemir, N., Solgun, M., Aktay, Ş.: Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry. 76(8), (2016).
Öz
Kaynakça
- [1] Bulut, Ş.: D-homothetic deformation on almost contact B-metric manifolds. J. of Geo. 110(23), (2019).
- [2] Chinea, D., Gonzalez, C.: A classification of almost contact metric manifolds. An.Sti.Univ."Al.I.Cuza"Iasi. 30, 75-79 (1984).
- [3] Dixmier, J.: Sur les representations unitaires des groupes de Lie nilpotentes III. Canadian Journal of Mathematics. 10, 321-348 (1958).
- [4] Ganchev, G., Borisov, A.: Note on almost contact manifolds with Norden metric. Compt. Rend. Acad. Bulg. Sci. 39, 31-34 (1986).
- [5] Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric. Mathematica Balkanica. 7, 261-276 (1993).
- [6] Manev, M.: Curvature properties on some classes of almost contact manifolds with B-metric. Compt. Rend. Acad. Bulg. Sci. 65 (4), 283-290 (2012).
- [7] Manev, H.: On the structure tensors of almost of contact B-metric Manifolds. Filomat. 29(3), 427-436 (2015).
- [8] Morimoto, A.: On normal almost contact structures. J. Math. Soc. Japan. 15, 420-436 (1963).
- [9] Özdemir, N., Solgun, M., Aktay, Ş.: Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry. 76(8), (2016).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Ekim 2020 |
| Kabul Tarihi | 16 Ağustos 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 13 Sayı: 2 |
