Pseudo-Quasi Conformal Curvature Tensor on Normal Paracontact Metric Space Forms

In the present paper we have studied the curvature tensor of a normal paracontact metric manifoldsatisfying the conditions R(ξ, X)$\overline C$ = 0, $\overline C$(ξ, X)S = 0, $\overline C$(ξ, X)P = 0, $\overline C$(ξ, X)$\overline Z$ = 0 and pseudo quasi conformalflat, where R, P, S , $\overline Z$ and $\overline C$ are the Riemannian curvature, projective curvature, Ricci, concircular curvature andpseudo-quasi conformal curvature tensors, respectively

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[1] Atc¸eken, M., Yıldırım, U¨ ., Almost C(α)-manifolds satisfying certain curvature conditions, Advanced Studies in Contemporary Mathematics, 26(3)(2016), 567–578. 1

[2] Atc¸eken, M., Yıldırım, U¨ ., On almost C(α)-manifolds satisfying certain conditions on quasi-conformal curvature tensor, Proceedings of the Jangjeon Mathematical Society, 19(1)(2016), 115–124. 1

[3] Chaturverdi, B.B., Gupta, B.K., Quasi-conformal curvature tensor of generalized Sasakian space forms, Fact Universitatis NISˇ , Ser. Math. Inform., 35(1)(2020), 89–99.

[4] Kenayuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99(1985), 173–187. 1

[5] Murthy, B., Vanketesha., On 3-dimensional pseudo quasi conformal curvature tensor on (LCS )n-manifolds, Open Acces Library Journal, 6(2019), e5474.

[6] Pandey, H.B., Kumar, A., Anti invariant submanifolds of almost paracontact manifolds, Indian J. Pure Appl. Math., 16(6)(1985), 586–590. 1

[7] Prakasha, D.G., Shivamurthy, T.R, Kakasab, M., On the pseudo quasi conformal curvature tensor of P-Sasakian manifold, Electronic Journal of Mathematical Analysis and Applications, 5(2)(2017), 147–155. 1

[8] Shaikh, A.A., Hui, S. K., On quasi-conformally flat almost pseudo Ricci symmetric manifolds, Tamsui Oxford Journal of Mathematical Sci- ences. 26(2)(2010).

[9] Shaikh, A.A., Jana, S.K., A pseudo quasi conformal curvature tensor on a Riemannian manifold, South East Asian J. of Math. Sci.,4(1)(2005), 15–20. 1, 2

[10] Shaikh, A.A., Jana, A.K., Eyasmin, S., On weakly pseudo quasi conformally symmetric manifolds, Indian J. Math., 50(3)(2008), 515–518.

[11] Welyzko, J., On legendre curves in 3-dimensional normal almost paracontact metric manifold, Result. Math., 54(2009), 377–387. 1

[12] Welyczko, J., Slant curves in 3-dimensional normal paracontact metric manifolds, Mediterr. J. Math., 11(2014), 965–978. 1

[13] Yılmaz, H., On almost pseudo quasi conformally symmetric manifold, Boletinde la asociacion mathemtical Venezolan, 21(2)(2014), 69–85.

[14] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob., Anal. Geom., 36(2009), 37–60. 1