Yılmaz, Hülya Bağdatlı; Özen Zengin, Füsun; Uysal, S. Aynur On a semi symmetric metric connection with a special condition on a Riemannian manifold. (English) Zbl 1389.53024 Eur. J. Pure Appl. Math. 4, No. 2, 153-161 (2011). Summary: In this study, we consider a manifold equipped with semi symmetric metric connection whose the torsion tensor satisfies a special condition. We investigate some properties of the Ricci tensor and the curvature tensor of this manifold. We obtain a necessary and sufficient condition for the mixed generalized quasi-constant curvature of this manifold. Finally, we prove that if the manifold mentioned above is conformally flat, then it is a mixed generalized quasi-Einstein manifold and we prove that if the sectional curvature of a Riemannian manifold with a semi symmetric metric connection whose the special torsion tensor is independent from orientation chosen, then this manifold is of a mixed generalized quasi constant curvature. Cited in 4 Documents MSC: 53B15 Other connections 53B20 Local Riemannian geometry 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:semi symmetric metric connection; generalized quasi-Einstein manifold; mixed generalized quasi constant curvature manifold; mixed generalized quasi-Einstein manifold PDFBibTeX XMLCite \textit{H. B. Yılmaz} et al., Eur. J. Pure Appl. Math. 4, No. 2, 153--161 (2011; Zbl 1389.53024) Full Text: Link References: [1] A Bhattacharyya and T De. On mixed generalized quasi-Einstein manifolds. Diff. Geo.- Dym Systm. A., 40-46, 9, 2007. · Zbl 1159.53324 [2] U C De and J Sengupta. On a type of semi symmetric metric connection on an almost contact metric manifold, Facta Universitatis (NIŠ) , Ser. Math. Inform., 87-96, 16, 2001. · Zbl 1060.53015 [3] U C De and B K De. Some properties of a semi symmetric metric connection on a Riemannian manifold. Istanbul Univ. Fen Fak. Mat. Derg., pp. 111-117, 54, 1995. · Zbl 0909.53011 [4] U C De and S C Biswas. On a type of semi symmetric metric connection on a Riemannian manifold. Publ. Inst. Math. (Beograd) (N. S.), 90-96, 61, 75, 1997. · Zbl 0999.53022 [5] U C De and G C Ghosh. On generalized quasi-Einstein manifolds. Kyungpook Math. J., 607-615, 44, 4, 2004. · Zbl 1076.53509 [6] T Imai. Notes on semi symmetric metric connections. Tensor (N.S.), 293-296, 24, 1972. · Zbl 0251.53038 [7] S Kobayashi and K Nomizu. Foundations of Differential Geometry. W. Interscience Pub- lishers, New York, 1963. · Zbl 0119.37502 [8] C Murathan and C Özgür. Riemannian manifolds with semi-symmmetric metric connection satisfying some semisymmetry conditions. Proceedings of the Estonian Academy of Sciences, 210-216, 57, 4, 2008. REFERENCES161 · Zbl 1218.53018 [9] E Pak. On the pseudo-Riemannian spaces. J. Korean Math. Soc., 23-31, 6,1969. [10] L Tamássy and T Q Binh. On the non-existence of certain connections with torsion and of constant curvature. Publ. Math. Debrecen, 283-288, 36, 1989. · Zbl 0696.53010 [11] K Yano. On semi symmetric metric connection. Rev. Roumaine, Math. Pures Appl., 15791586,15, 1970. · Zbl 0213.48401 [12] K Yano and M Kon. Structures on manifolds. Series in Pure Math., World Scientific, 1984. [13] F Ö Zengin S A Uysal and S A Demirbag. On sectional curvature of a Riemannian manifold with semi-symmetric connection. Annales Polonici Mathematici, (in print). · Zbl 1215.53018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.