Research Article
BibTex RIS Cite

BAZI LİE CEBİRLERİ ÜZERİNDE HEMEN-HEMEN KONTAKT YAPILAR

Year 2022, Volume: 10 Issue: 2, 75 - 81, 23.08.2022

Şirin Aktay

https://doi.org/10.20290/estubtdb.1006054

Abstract

Bu çalışmada bazı 7 boyutlu reel Lie cebirleri üzerinde yapının vektör alanı paralel olacak şekilde hemen hemen kontakt metrik yapıların olmadığı gösterilmiştir.

Keywords

7-boyutlu nilpotent Lie cebri hemen-hemen kontakt metrik yapı paralel vektör alanı

Supporting Institution

Eskişehir Teknik Üniversitesi

Project Number

19ADP178

References

  • [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.

ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS

Year 2022, Volume: 10 Issue: 2, 75 - 81, 23.08.2022

Şirin Aktay

https://doi.org/10.20290/estubtdb.1006054

Abstract

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.

Keywords

7-dimensional nilpotent Lie algebra almost contact metric structure parallel vector field

Project Number

19ADP178

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Şirin Aktay 0000-0003-2792-3481

Project Number 19ADP178
Publication Date August 23, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Aktay, Ş. (2022). ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 10(2), 75-81. https://doi.org/10.20290/estubtdb.1006054
AMA Aktay Ş. ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. August 2022;10(2):75-81. doi:10.20290/estubtdb.1006054
Chicago Aktay, Şirin. “ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 10, no. 2 (August 2022): 75-81. https://doi.org/10.20290/estubtdb.1006054.
EndNote Aktay Ş (August 1, 2022) ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10 2 75–81.
IEEE Ş. Aktay, “ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 2, pp. 75–81, 2022, doi: 10.20290/estubtdb.1006054.
ISNAD Aktay, Şirin. “ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10/2 (August 2022), 75-81. https://doi.org/10.20290/estubtdb.1006054.
JAMA Aktay Ş. ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10:75–81.
MLA Aktay, Şirin. “ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 2, 2022, pp. 75-81, doi:10.20290/estubtdb.1006054.
Vancouver Aktay Ş. ALMOST CONTACT STRUCTURES ON SOME LIE ALGEBRAS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10(2):75-81.