Some Applications of the Concircular Mappings on the Weyl Manifolds

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.

Weyl Manifoldları Üzerindeki Concircular Tasvirlerin Bazı Uygulamaları

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

1. Besse, A.L. 1987. Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 10.
2. Eisenhart, L.P. 1927. Non-Riemannian Geometry, American Math.Society Colloqium Publications, Vol.8.
3. Liang, Y. 1994. On semi symmetric recurrent metric S-concircular connections, Journal of Mathematical Study, 104-108.
4. Miron, R. 1968. Mouvements conformes dans les espaces W_n, Tensor N.S., 19, 33-41.
5. Murgescu, V. 1968. Espaces de Weyl a torsion et leurs representations conformes, Ann. Sci. Univ. Timisoara, 221-228.
6. Norden, A. 1976. Affinely connected spaces, GRMFL, Moscow (in Russian).
7. 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.
8. Ozdeger, A. and Senturk, Z. 2002. Generalized Circles in Weyl Spaces and their conformal mapping, Publ. Math. Debrecen, 60, 1-2 & 75-87.

9. Scholz, E. 2008. Weyl geometry in late 20th century physics, arxiv.org/math arxiv, 1111.3220.
10. Unal, F. Nurcan and Uysal, A. 2005. Weyl Manifolds with semi symmetric connections, Mathematical and Computational Applications, 10, 351-358.