Abstract
In this paper, two applications of concircular
mappings on the Weyl manifolds are given: Firstly, a necessary and sufficient
condition for an Einstein-Weyl manifold to be concircularly Ricci-flat is
obtained. Secondly, after defining a special type of semi-symmetric non-metric
connection which is called S -concircular, some properties of the Weyl manifold
with a vanishing curvature tensor with respect to such a connection are
examined.
References
- Besse, A.L. 1987. Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 10.
- Eisenhart, L.P. 1927. Non-Riemannian Geometry, American Math.Society Colloqium Publications, Vol.8.
- Liang, Y. 1994. On semi symmetric recurrent metric S-concircular connections, Journal of Mathematical Study, 104-108.
- Miron, R. 1968. Mouvements conformes dans les espaces W_n, Tensor N.S., 19, 33-41.
- Murgescu, V. 1968. Espaces de Weyl a torsion et leurs representations conformes, Ann. Sci. Univ. Timisoara, 221-228.
- Norden, A. 1976. Affinely connected spaces, GRMFL, Moscow (in Russian).
- Nurcan, F. 2014. A Necessary and Sufficient Condition on the Weyl Manifolds admitting a semi symmetric non-metric connection to be S-concircular, 12. National Geometry Symposium, Bilecik University.
- Ozdeger, A. and Senturk, Z. 2002. Generalized Circles in Weyl Spaces and their conformal mapping, Publ. Math. Debrecen, 60, 1-2 & 75-87.
- Scholz, E. 2008. Weyl geometry in late 20th century physics, arxiv.org/math arxiv, 1111.3220.
- Unal, F. Nurcan and Uysal, A. 2005. Weyl Manifolds with semi symmetric connections, Mathematical and Computational Applications, 10, 351-358.
Abstract
Bu çalışmada, Weyl manifoldları üzerindeki
concircular tasvirlerin iki uygulaması verilmiştir: İlk olarak, Einstein-Weyl
manifoldunun concircular Ricci düz olabilmesi için bir gerek-yeter şart elde
edilmiştir. Daha sonra da, S -concircular olarak adlandırılan özel tipteki bir
yarı simetrik non-metrik konneksiyon tanımlanarak, böyle bir konneksiyona göre
sıfırlanan eğrilik tensörüne sahip Weyl manifoldunun bazı özellikleri
incelenmiştir
Keywords
Weyl manifoldu yarı simetrik non-metrik S -concircular konneksiyon sıfırlanan eğrilik tensörü
References
- Besse, A.L. 1987. Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 10.
- Eisenhart, L.P. 1927. Non-Riemannian Geometry, American Math.Society Colloqium Publications, Vol.8.
- Liang, Y. 1994. On semi symmetric recurrent metric S-concircular connections, Journal of Mathematical Study, 104-108.
- Miron, R. 1968. Mouvements conformes dans les espaces W_n, Tensor N.S., 19, 33-41.
- Murgescu, V. 1968. Espaces de Weyl a torsion et leurs representations conformes, Ann. Sci. Univ. Timisoara, 221-228.
- Norden, A. 1976. Affinely connected spaces, GRMFL, Moscow (in Russian).
- Nurcan, F. 2014. A Necessary and Sufficient Condition on the Weyl Manifolds admitting a semi symmetric non-metric connection to be S-concircular, 12. National Geometry Symposium, Bilecik University.
- Ozdeger, A. and Senturk, Z. 2002. Generalized Circles in Weyl Spaces and their conformal mapping, Publ. Math. Debrecen, 60, 1-2 & 75-87.
- Scholz, E. 2008. Weyl geometry in late 20th century physics, arxiv.org/math arxiv, 1111.3220.
- Unal, F. Nurcan and Uysal, A. 2005. Weyl Manifolds with semi symmetric connections, Mathematical and Computational Applications, 10, 351-358.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | August 31, 2019 |
| Published in Issue | Year 2019 Volume: 12 Issue: 2 |