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Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras

Year 2022, , 117 - 121, 30.09.2022
https://doi.org/10.32323/ujma.1169830

Abstract

It is known that from a given almost Hermitian structure on a simply connected Liegroup, one can obtain left-invariant almost Hermitian structure on its Lie algebra.In this work, we consider Mubarakzyanov’s classification of four-dimensional realLie algebras and evaluate the existence of almost Hermitian structures on four dimensional decomposable real Lie algebras. In particular, we focus on almost Kaehlerian and Hermitian structures on these Lie algebras.

References

  • [1] A. Gray, L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura. Appl., 123 (1980), 35-58.
  • [2] A. Gray, Some examples of almost Hermitian manifolds, Illinois J. Math., 10(2) (1966), 353-366.
  • [3] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds , Birkh ¨ auser, Switzerland, 2002.
  • [4] N. Özdemir, M. Solgun, S¸ . Aktay, Almost contact metric structures on 5-dimensional nilpotent Lie algebras, Symmetry, 8(8) (2016), 76.
  • [5] N. Ozdemir, M. Solgun, S¸ . Aktay, Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras, Fundam. J. Math., 3(2) (2020), 175-184.
  • [6] N. Ozdemir, S¸ . Aktay, M. Solgun, Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 326-333.
  • [7] G. M. Mubarakzyanov, On solvable Lie algebras, Izv. Vyssh. Uchebn. Zaved. Mat., 1 (1963), 114-123.
  • [8] R. O. Popovych, V. M. Boyko, M. O. Nesterenko, M. W. Lutfullin, Realizations of real low-dimensional Lie algebras, J. Phys. A Math. Gen., 36(26) (2003), 7337.
Year 2022, , 117 - 121, 30.09.2022
https://doi.org/10.32323/ujma.1169830

Abstract

References

  • [1] A. Gray, L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura. Appl., 123 (1980), 35-58.
  • [2] A. Gray, Some examples of almost Hermitian manifolds, Illinois J. Math., 10(2) (1966), 353-366.
  • [3] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds , Birkh ¨ auser, Switzerland, 2002.
  • [4] N. Özdemir, M. Solgun, S¸ . Aktay, Almost contact metric structures on 5-dimensional nilpotent Lie algebras, Symmetry, 8(8) (2016), 76.
  • [5] N. Ozdemir, M. Solgun, S¸ . Aktay, Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras, Fundam. J. Math., 3(2) (2020), 175-184.
  • [6] N. Ozdemir, S¸ . Aktay, M. Solgun, Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 326-333.
  • [7] G. M. Mubarakzyanov, On solvable Lie algebras, Izv. Vyssh. Uchebn. Zaved. Mat., 1 (1963), 114-123.
  • [8] R. O. Popovych, V. M. Boyko, M. O. Nesterenko, M. W. Lutfullin, Realizations of real low-dimensional Lie algebras, J. Phys. A Math. Gen., 36(26) (2003), 7337.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Solgun 0000-0002-2275-7763

Publication Date September 30, 2022
Submission Date September 1, 2022
Acceptance Date September 24, 2022
Published in Issue Year 2022

Cite

APA Solgun, M. (2022). Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras. Universal Journal of Mathematics and Applications, 5(3), 117-121. https://doi.org/10.32323/ujma.1169830
AMA Solgun M. Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras. Univ. J. Math. Appl. September 2022;5(3):117-121. doi:10.32323/ujma.1169830
Chicago Solgun, Mehmet. “Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras”. Universal Journal of Mathematics and Applications 5, no. 3 (September 2022): 117-21. https://doi.org/10.32323/ujma.1169830.
EndNote Solgun M (September 1, 2022) Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras. Universal Journal of Mathematics and Applications 5 3 117–121.
IEEE M. Solgun, “Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras”, Univ. J. Math. Appl., vol. 5, no. 3, pp. 117–121, 2022, doi: 10.32323/ujma.1169830.
ISNAD Solgun, Mehmet. “Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras”. Universal Journal of Mathematics and Applications 5/3 (September 2022), 117-121. https://doi.org/10.32323/ujma.1169830.
JAMA Solgun M. Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras. Univ. J. Math. Appl. 2022;5:117–121.
MLA Solgun, Mehmet. “Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras”. Universal Journal of Mathematics and Applications, vol. 5, no. 3, 2022, pp. 117-21, doi:10.32323/ujma.1169830.
Vancouver Solgun M. Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras. Univ. J. Math. Appl. 2022;5(3):117-21.

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