A survey on different types of generalized recurrency on the weyl manifold

Yıl 2013, Cilt: 25 Sayı: 4, 192 - 201, 09.03.2014

Füsun Nurcan Baştan

Öz

Hayden [1] introduced a semi symmetric metric connection on the Rie-mannian manifolds. This definition was developed by Yano [2] and Imai [3-4]. In [5], we examined the Weyl manifold, which is the generalization of the Riemannian manifold, admitting a semi symmetric connection. Pavel Enghish [6-7] examined the recurrency and generalized recurrency on the Riemannian manifolds with respect to symmetric and semi symmetric connections.

The aim of this paper is to obtain the relations between different types of the Weyl manifolds under some special conditions which are concerning the definitions of generalized recurrency, generalized conformally recurrency and generalized projectively recurrency.

Anahtar Kelimeler

Weyl manifold; semi symmetric connection; conformal curvature tensor; projective curvature tensor; generalized recurrency

Kaynakça

• (l) Hayden, H.A.Z Subspaces of a space with torsion, Proc. London Math. Soc, 1932, 34, 27—50.
• (2) Yano7 K., On semi symmetric metric connection. Rev. Roumaine Math. Pure Appl., 1970. 15, 1579-1586. l3] Imai, T., Hypersurfaces of a Riemannian manifold with semi symmetric metric connection, Tensor N.S., 1972, 23, 300—306. l4] Imai,T., Notes on semi symmetric metric connections, Tensor N.S., 1972, 24, 293—296.
• Unal, F., Uysal, A., Weyl Manifolds with semi symmetric connections, Math—
• ematical and Computational Applications, 2005, Vol.10, No:3.
• l6] Enghis, P., Relations between the tensors of various curvatures of a D
• connection, Proc. Of Symposium in Geometry (Cluj—Napoca and Tirgu—
• Enghis, P., Boer, M., Generalized recurrency in spaces with aşine connec
• tion, Studia Univ. Babes—Bolyai, Math” 1988, 33, 74—79.
• Norden, A., Aşinely connected spaces, GRMFL, Moscow (in Russian), 1976.