Öz
Bu çalışmada bazı 7 boyutlu reel Lie cebirleri üzerinde yapının vektör alanı paralel olacak şekilde hemen hemen kontakt metrik yapıların olmadığı gösterilmiştir.
Anahtar Kelimeler
7-boyutlu nilpotent Lie cebri hemen-hemen kontakt metrik yapı paralel vektör alanı
Destekleyen Kurum
Eskişehir Teknik Üniversitesi
Proje Numarası
19ADP178
Kaynakça
- [1] Calvaruso G. Three-dimensional homogeneous almost contact metric structures. J Geom Phys, 2013; 6, 60-73.
- [2] Andrada A, Fino A, Vezzoni, L. A class of Sasakian 5-manifolds. Transform Groups, 2009; 3-14: 493-512.
- [3] Calvaruso G, Fino A. Five-dimensional K-contact Lie algebras. Monatsh Math, 2012; 167, 35-59.
- [4] Özdemir N, Solgun M, Aktay Ş. Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry-Basel, 2016; 8, 76; doi:10.3390/sym8080076.
- [5] Özdemir N, Aktay Ş, Solgun M. Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras. Commun Fac Sci Univ Ank Ser A1 Math Stat, 2019; 68(1) 326-333.
- [6] Gong MP. Classification of nilpotent Lie algebras of dimension 7. PhD, University of Waterloo, Waterloo, Ontario, Canada, 1998.
- [7] Alvarez MA, Rodriguez-Vallarte M. C, Salgado G. Contact nilpotent Lie algebras. Proc Amer Math Soc, 2017; 145, 1467-1474.
- [8] Smolentsev NK. Invariant pseudo-Sasakian and K-contact structures on seven dimensional nilpotent Lie groups. arXiv: 1701.04142v1 [math DG]
- [9] Kutsak S. Invariant contact structures on 7-dimensional nilmanifolds. Geom Dedicata, 2014; 172, 351-361.
- [10] Chinea D, Gonzales C. A classification of almost contact metric manifolds. Ann Mat Pura Appl, 1990; 4-156: 15-36.
- [11] Alexiev V, Ganchev G. On the classification of the almost contact metric manifolds, Math and Educ in Math, Proc of the XV Spring Conf of UBM, Sunny Beach, Bulgaria, 155, 1986.
- [12] Blair DE. Riemannian Geometry of Contact and Symplectic Manifolds. 2nd ed. Birkha ̈user, Switzerland, 2002.
- [13] Dixmier J. Sur les representations unitaires des groupes de Lie nilpotentes III. Canad J Math, 1958; 10, 321-348.
Öz
In this manuscript, we show that there are no almost contact structures with parallel characteristic vector field on certain 7 dimensional Lie algebras over the real field.
Anahtar Kelimeler
7-dimensional nilpotent Lie algebra almost contact metric structure parallel vector field
Proje Numarası
19ADP178
Kaynakça
- [1] Calvaruso G. Three-dimensional homogeneous almost contact metric structures. J Geom Phys, 2013; 6, 60-73.
- [2] Andrada A, Fino A, Vezzoni, L. A class of Sasakian 5-manifolds. Transform Groups, 2009; 3-14: 493-512.
- [3] Calvaruso G, Fino A. Five-dimensional K-contact Lie algebras. Monatsh Math, 2012; 167, 35-59.
- [4] Özdemir N, Solgun M, Aktay Ş. Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry-Basel, 2016; 8, 76; doi:10.3390/sym8080076.
- [5] Özdemir N, Aktay Ş, Solgun M. Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras. Commun Fac Sci Univ Ank Ser A1 Math Stat, 2019; 68(1) 326-333.
- [6] Gong MP. Classification of nilpotent Lie algebras of dimension 7. PhD, University of Waterloo, Waterloo, Ontario, Canada, 1998.
- [7] Alvarez MA, Rodriguez-Vallarte M. C, Salgado G. Contact nilpotent Lie algebras. Proc Amer Math Soc, 2017; 145, 1467-1474.
- [8] Smolentsev NK. Invariant pseudo-Sasakian and K-contact structures on seven dimensional nilpotent Lie groups. arXiv: 1701.04142v1 [math DG]
- [9] Kutsak S. Invariant contact structures on 7-dimensional nilmanifolds. Geom Dedicata, 2014; 172, 351-361.
- [10] Chinea D, Gonzales C. A classification of almost contact metric manifolds. Ann Mat Pura Appl, 1990; 4-156: 15-36.
- [11] Alexiev V, Ganchev G. On the classification of the almost contact metric manifolds, Math and Educ in Math, Proc of the XV Spring Conf of UBM, Sunny Beach, Bulgaria, 155, 1986.
- [12] Blair DE. Riemannian Geometry of Contact and Symplectic Manifolds. 2nd ed. Birkha ̈user, Switzerland, 2002.
- [13] Dixmier J. Sur les representations unitaires des groupes de Lie nilpotentes III. Canad J Math, 1958; 10, 321-348.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Proje Numarası | 19ADP178 |
| Yayımlanma Tarihi | 23 Ağustos 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 10 Sayı: 2 |