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Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras

Year 2023, Volume: 11 Issue: 2, 206 - 217, 31.10.2023

Abstract

The object of our investigations is to classify 5-dimensional nilpotent Lie algebras with two different Riemannian $\Pi-$structures. It is shown that the Lie groups corresponding to the Lie algebras $\mathfrak{g} _{i}$ equipped with two different Riemannian $\Pi-$structures is not para-Sasaki-like. Moreover, we investigate whether the considered manifolds admit Ricci-like solitons and whether they are $\eta-$Einstein manifolds.

References

  • [1] H. Manev, M. Manev, Para-Ricci-like solitons on Riemannian manifolds with almost paracontact structure and almost paracomplex structure. Mathematics, 9(14) (2021), 1704.
  • [2] H. Manev, Para-Ricci-like solitons with vertical potential on para-Sasaki-like Riemannian Õ􀀀manifolds, Symmetry, 13 (2021), 2267.
  • [3] H. Manev, M. Manev, Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian manifolds, Mathematics, 10(4) (2022), 651.
  • [4] M. Manev, M. Staikova, On almost paracontact Riemannian manifolds of type (n;n), J. Geom., 72 (2001), 108-114.
  • [5] H.G. Nagaraja, C.R. Premalatha, Ricci solitons in Kenmotsu manifolds, J. Math. Anal., 3(2) (2012), 18-24.
  • [6] S. Ivanov, H. Manev and M. Manev, Para-Sasaki-like Riemannian manifolds and new Einstein metrics, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas, 115 (2021), 112.
  • [7] H. D. Cao, Recent progress on Ricci solitons, Adv. Lect. Math. (ALM), 11 (2009), 1-38.
  • [8] J. Dixmier, Sur les reprentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
  • [9] S. Kaneyuki, F.L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [10] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., 36 (2009), 37-60.
  • [11] A. Ali, F. Mofarreh, D. S. Patra, Geometry of almost Ricci solitons on paracontact metric manifolds, Quaestiones Mathematicae, 45(8) (2022), 1167-1180.
Year 2023, Volume: 11 Issue: 2, 206 - 217, 31.10.2023

Abstract

References

  • [1] H. Manev, M. Manev, Para-Ricci-like solitons on Riemannian manifolds with almost paracontact structure and almost paracomplex structure. Mathematics, 9(14) (2021), 1704.
  • [2] H. Manev, Para-Ricci-like solitons with vertical potential on para-Sasaki-like Riemannian Õ􀀀manifolds, Symmetry, 13 (2021), 2267.
  • [3] H. Manev, M. Manev, Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian manifolds, Mathematics, 10(4) (2022), 651.
  • [4] M. Manev, M. Staikova, On almost paracontact Riemannian manifolds of type (n;n), J. Geom., 72 (2001), 108-114.
  • [5] H.G. Nagaraja, C.R. Premalatha, Ricci solitons in Kenmotsu manifolds, J. Math. Anal., 3(2) (2012), 18-24.
  • [6] S. Ivanov, H. Manev and M. Manev, Para-Sasaki-like Riemannian manifolds and new Einstein metrics, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas, 115 (2021), 112.
  • [7] H. D. Cao, Recent progress on Ricci solitons, Adv. Lect. Math. (ALM), 11 (2009), 1-38.
  • [8] J. Dixmier, Sur les reprentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
  • [9] S. Kaneyuki, F.L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [10] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., 36 (2009), 37-60.
  • [11] A. Ali, F. Mofarreh, D. S. Patra, Geometry of almost Ricci solitons on paracontact metric manifolds, Quaestiones Mathematicae, 45(8) (2022), 1167-1180.
There are 11 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Şenay Bulut

Vildan Korucu Akan 0009-0007-8501-9753

Publication Date October 31, 2023
Submission Date May 5, 2023
Acceptance Date August 8, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Bulut, Ş., & Korucu Akan, V. (2023). Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras. Konuralp Journal of Mathematics, 11(2), 206-217.
AMA Bulut Ş, Korucu Akan V. Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras. Konuralp J. Math. October 2023;11(2):206-217.
Chicago Bulut, Şenay, and Vildan Korucu Akan. “Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras”. Konuralp Journal of Mathematics 11, no. 2 (October 2023): 206-17.
EndNote Bulut Ş, Korucu Akan V (October 1, 2023) Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras. Konuralp Journal of Mathematics 11 2 206–217.
IEEE Ş. Bulut and V. Korucu Akan, “Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras”, Konuralp J. Math., vol. 11, no. 2, pp. 206–217, 2023.
ISNAD Bulut, Şenay - Korucu Akan, Vildan. “Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras”. Konuralp Journal of Mathematics 11/2 (October 2023), 206-217.
JAMA Bulut Ş, Korucu Akan V. Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras. Konuralp J. Math. 2023;11:206–217.
MLA Bulut, Şenay and Vildan Korucu Akan. “Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras”. Konuralp Journal of Mathematics, vol. 11, no. 2, 2023, pp. 206-17.
Vancouver Bulut Ş, Korucu Akan V. Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras. Konuralp J. Math. 2023;11(2):206-17.
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