On a Quarter-Symmetric Projective Conformal Connection

Year 2017, Volume: 10 Issue: 2, 37 - 45, 29.10.2017

Wanxiao Tang Tal Yun Ho Fengyun Fu Peibiao Zhao

https://doi.org/10.36890/iejg.545046

Abstract

We introduce a class of quarter-symmetric projective conformal connections, and study the

geometrical properties of a manifold associated with this connection. The Schur’s theorem

corresponding to the quarter-symmetric projective conformal connection is derived.

Keywords

quarter-symmetric projective conformal connection, conjugate symmetry, constant curvature

References

• [1] De, U. C. and Biswas, S. C., Quarter-symmetric metric connection in an SP-Sasakian manifold, Commun. Fac. Sci. Univ. Ank. Series Al.. 46(1997), 49-56.
• [2] De, U. C. and Biswas, S. C., On a type of semi-symmetric metric connection on a Riemannian manifold, Publ. Inst. Math.(Beograd)(N. S. ). 61(1997), no.75, 90-96.
• [3] De, U. C. and Kamilya, D., Hypersurfaces of Kenmotsu manifolds endowed with a quarter-symmetric non-metric connection , Kuwait J. Sci. Eng.. 39( 2012), no.1A, 43-56.
• [4] De, U. C. and Mondal, A. K., Quarter-symmetric metric connection on 3-dimensional quasi-Sasakian manifolds, SUT Journal of Mathematics. 46(2010), no.1, 35-52.
• [5] De, U. C. and Sengupta, J., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Bull. Cal. Math. Soc.. 92(2000),375-884.
• [6] Fridman, A. and Schouten, J. A., Uber die Geometric der halb-symmerischen Ubertrngungen, Math.Zeitschift. 21(1924), 211-233.
• [7] Han, Y. L., Ho, Tal Yun. and Zhao, P. B., Some invariants of quarter-symmetric metric connections under the projective transformation, Filomat. 27(2013), no.4, 679-691.
• [8] Han, Y. L., Ho, Tal Yun. and Zhao, P. B., A Schur’s lemma based on a semi-symmetric non-metric connection, International Journal of Geometry. 5(2016), no.1, 47-53.
• [9] Han, Y. L. and Zhao, P. B., A Class of nearly sub-Weyl and sub-Lyra Manifolds, accepted in International Electronic Journal of Geometry. (2016).
• [10] Hayden, H. A., Subspace of space with torsion, Proc. of London Math. Soc.. 24 (1932), 27-50.
• [11] Stepanova, E. S., Dual symmetric statistical manifold. J. of Mathematical Sciences. 147(2007), no.1, 6507-6509.
• [12] Yano, K., On semi-symmetric metric connection, Rev. Roun. Math. Purest. Appl.. 15(1971), 1579-1586.
• [13] Yano, K. and Imai, J., Quarter-symmetric metric connection and their curvature tensors, Tensor. N. S.. 38(1982), 13-18.
• [14] Ho, Tal Yun., On a semi-symmetric non-metric connection satisfying the Schur’s theorem on a Riemannian manifold, arXiv:1212,4748v1.
• [15] Ho, Tal Yun., On the projective semi-symmetric connection and the conformal semi-symmetric connection on the Riemannian manifold, J. of Kim Il Sung University (Natural Science). 2(2013), no.2, 3-10.
• [16] Ho, Tal Yun., An, Jae Hyon and An, Chang Gil., Some properties of mutual connection of semi-symmetric metric connection and its dual connection in a Riemannian manifold, Acta Scientiarum Naturalium Universtatis Nankaiensts. 46(2013), no.4, 1-8.
• [17] Ho, Tal Yun., Jen, Cholyong and Jin, Guangzhi., A semi-symmetric projective conformal connection satisfying the Schur’s theorem on a Riemannian manifold, J. of Yanbian University (Natural Science). 40(2014), no.4, 290-294.
• [18] Zhao, P. B., Some properties of projective semi-symmetric connections, International Mathematical Forum. 3(2008), no. 7, 341-347.
• [19] Zhao, P. B. and Song, H. Z., An invariant of the projective semi-symmetric connection, Chinese Quarterly J. of Math.. 17(2001), no. 4, 48-52.
• [20] Zhao, P. B., Song, H. Z. and Yang, X. P., Some invariant properties of the semi-symmetric metric recurrent connections and curvature tensor expressions, Chinese Quarterly J. of Math.. 19(2004), no. 4, 355-361.