Abstract
In this study, we examine the existence of quasi-Sasakian structures on nilpotent Lie algebras of dimension five. In addition, we give some results about left invariant quasi-Sasakian structures on Lie groups of dimension five, whose Lie algebras are nilpotent. Moreover, subclasses of quasi-Sasakian structures are studied for some certain classes.
Keywords
5-dimensional nilpotent Lie algebra almost contact metric structure quasi-Sasakian structure
References
- Morimoto, A. On Normal Almost Contact Structures. J. Math. Soc. Japan, 15 (4), (1963) 420-436.
- Andrada, A., Fino, A., Vezzoni, L. 2009. A Class of Sasakian 5-Manifolds. Transform. Groups, 14 (3), 493-512.
- Calvaruso, G., Fino, A., Five-dimensional K-contact Lie algebras. Monatsh Math., 167, (2012) 35-59.
- Özdemir, N., Solgun, M., Aktay, Ş., Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras. Symmetry, 76 (8), (2016) 13 pages.
- Chinea, D., Gonzales, C., A Classification of Almost Contact Metric Manifolds. Ann. Mat. Pura Appl., 156 (4), (1990) 15-36.
- Alexiev, V., Ganchev, G., 1986. On the Classification of the Almost Contact Metric Manifolds. Math. and Educ. in Math., Proc. of the XV Spring Conf. of UBM, Sunny Beach, 155-161.
- Dixmier, J., Sur les Representations Unitaires des Groupes de Lie Nilpotentes III. Canad. J. Math., 10, (1958) 321-348.
- Gong, M.P., Classification of nilpotent Lie algebras of dimension 7, University of Waterloo, Ph.D. Thesis, 173 pages, Waterloo, Ontario, Canada.1998.
- de Graaf, W. A., Classification of 6-dimensional Nilpotent Lie Algebras Over Fields of Characteristic not 2. J. Algebra, 309, (2007) 640-653.
- Blair, D.E., The Theory of Quasi-Sasakian Structures. J. Differential Geometry, 1, (1967) 331-345.
Abstract
References
- Morimoto, A. On Normal Almost Contact Structures. J. Math. Soc. Japan, 15 (4), (1963) 420-436.
- Andrada, A., Fino, A., Vezzoni, L. 2009. A Class of Sasakian 5-Manifolds. Transform. Groups, 14 (3), 493-512.
- Calvaruso, G., Fino, A., Five-dimensional K-contact Lie algebras. Monatsh Math., 167, (2012) 35-59.
- Özdemir, N., Solgun, M., Aktay, Ş., Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras. Symmetry, 76 (8), (2016) 13 pages.
- Chinea, D., Gonzales, C., A Classification of Almost Contact Metric Manifolds. Ann. Mat. Pura Appl., 156 (4), (1990) 15-36.
- Alexiev, V., Ganchev, G., 1986. On the Classification of the Almost Contact Metric Manifolds. Math. and Educ. in Math., Proc. of the XV Spring Conf. of UBM, Sunny Beach, 155-161.
- Dixmier, J., Sur les Representations Unitaires des Groupes de Lie Nilpotentes III. Canad. J. Math., 10, (1958) 321-348.
- Gong, M.P., Classification of nilpotent Lie algebras of dimension 7, University of Waterloo, Ph.D. Thesis, 173 pages, Waterloo, Ontario, Canada.1998.
- de Graaf, W. A., Classification of 6-dimensional Nilpotent Lie Algebras Over Fields of Characteristic not 2. J. Algebra, 309, (2007) 640-653.
- Blair, D.E., The Theory of Quasi-Sasakian Structures. J. Differential Geometry, 1, (1967) 331-345.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | February 1, 2017 |
| Acceptance Date | December 13, 2017 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
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