Geodesic
Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection
Filomat, Tome 37 (2023) no. 14, p. 4715

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

As a natural consequence of the Levi-Civita connection on a Riemannian manifold, there is a Lie algebra structure on a Riemannian manifold. Lie Algebras and Lie Groups are the mathematical structure of continuous symmetries in physics. In this paper, semi-symmetric non-metric connection is considered instead of Levi-Civita connection of Riemann manifold, and accordingly the existence of algebraic structures is investigated. First, it is shown that there is not always a Lie algebra structure on a Riemannian manifold with a semi-symmetric non-metric connection. Then, necessary and sufficient conditions for Lie admissible algebra, pre-Lie algebra and post Lie algebra on a Riemann manifold with semi-symmetric non-metric connection are obtained depending on geometric terms. In addition, the cases of the Riemannian manifold with such algebraic structures according to the semi-symmetric non-metric connection being Einstein manifold and being flat manifold have been also investigated.
DOI : 10.2298/FIL2314715S
Classification : 53B20, 17D25;17D99
Keywords: Riemannian manifold, Lie algebra, pre-Lie algebra, Lie admissible algebra, post-Lie algebra, semi-symmetric non-metric connection 
Fulya Şahin; Bayram Şahin. Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection. Filomat, Tome 37 (2023) no. 14, p. 4715 . doi: 10.2298/FIL2314715S
@article{10_2298_FIL2314715S,
     author = {Fulya \c{S}ahin and Bayram \c{S}ahin},
     title = {Certain lie algebraic structures on {Riemannian} manifolds with semi-symmetric non-metric connection},
     journal = {Filomat},
     pages = {4715 },
     year = {2023},
     volume = {37},
     number = {14},
     doi = {10.2298/FIL2314715S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2314715S/}
}
TY  - JOUR
AU  - Fulya Şahin
AU  - Bayram Şahin
TI  - Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection
JO  - Filomat
PY  - 2023
SP  - 4715 
VL  - 37
IS  - 14
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2314715S/
DO  - 10.2298/FIL2314715S
LA  - en
ID  - 10_2298_FIL2314715S
ER  - 
%0 Journal Article
%A Fulya Şahin
%A Bayram Şahin
%T Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection
%J Filomat
%D 2023
%P 4715 
%V 37
%N 14
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2314715S/
%R 10.2298/FIL2314715S
%G en
%F 10_2298_FIL2314715S

Cité par Sources :