Almost Kaehlerian and Hermitian Structures on Four Dimensional Indecomposable Lie Algebras

Year 2022, Volume: 5 Issue: 3, 117 - 121, 30.09.2022

Mehmet Solgun

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.

Keywords

Almost Hermitian manifold, Hermitian scructure, Kaehlerian structure

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.