On the Pseudo-Quasi Conformal Curvature Tensor of a Normal Paracontact Metric Manifold
On the Pseudo-Quasi Conformal Curvature Tensor of a Normal Paracontact Metric Manifold
In the present paper we have studied the curvature tensor of a normal paracontact metric manifold satisfying the conditions $ R(\xi,X) \widetilde{C}=0 $, $ \widetilde{C}(\xi,X)S=0 $, $ \widetilde{C}(\xi,X)P=0 $, $ \widetilde{C}(\xi,X)\widetilde{Z}=0 $ and pseudo quasi conformal flat, where $ R $, $ P $, $ S $, $ \widetilde{Z} $ and $ \widetilde{C} $ are the Riemannian curvature, projective curvature, Ricci, concircular curvature and pseudo-quasi conformal curvature tensors, respectively.
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- At\c{c}eken, M., Y{\i}ld{\i}r{\i}m, \"{U}., {\em Almost $C(\alpha)$-manifolds satisfying certain curvature conditions}, Advanced Studies in Contemporary Mathematics, \textbf{26(3)}(2016), 567--578.
- At\c{c}eken, M., Y{\i}ld{\i}r{\i}m, \"{U}., {\em On almost $C(\alpha)$-manifolds satisfying certain conditions on quasi-conformal curvature tensor}, Proceedings of the Jangjeon Mathematical Society, \textbf{19(1)}(2016), 115--124.
- Chaturverdi, B.B., Gupta, B.K., {\em Quasi-conformal curvature tensor of generalized Sasakian space
forms}, Fact Universitatis $NI\check{S}$, Ser. Math. Inform.,
\textbf{35(1)}(2020), 89--99.
- Kenayuki, S., Williams, F.L., {\em Almost paracontact and parahodge structures on manifolds}, Nagoya Math. J., \textbf{99}(1985), 173--187.
- Murthy, B., Vanketesha., {\em On 3-dimensional pseudo quasi conformal curvature tensor on
$(LCS)_{n}$-manifolds}, Open Acces Library Journal,
\textbf{6}(2019), e5474.
- Pandey, H.B., Kumar, A., {\em Anti invariant submanifolds of almost paracontact
manifolds}, Indian J. Pure Appl. Math., \textbf{16(6)}(1985),
586--590.
- Prakasha, D.G., Shivamurthy, T.R, Kakasab, M., {\em On the pseudo quasi conformal curvature tensor of P-Sasakian
manifold}, Electronic Journal of Mathematical Analysis and
Applications, \textbf{5(2)}(2017), 147--155.
- Shaikh, A.A., Hui, S. K., {\em On quasi-conformally flat
almost pseudo Ricci symmetric manifolds}, Tamsui Oxford Journal of
Mathematical Sciences. \textbf{26(2)}(2010).
- Shaikh, A.A., Jana, S.K., {\em A pseudo quasi conformal curvature tensor on a Riemannian
manifold}, South East Asian J. of Math. Sci.,\textbf{4(1)}(2005),
15--20.
- Shaikh, A.A., Jana, A.K., Eyasmin, S., {\em On weakly pseudo quasi conformally symmetric
manifolds}, Indian J. Math., \textbf{50(3)}(2008), 515--518.
- Welyzko, J., {\em On legendre curves in 3-dimensional normal almost paracontact metric
manifold}, Result. Math., \textbf{54}(2009), 377--387.
- Welyczko, J., {\em Slant curves in 3-dimensional normal paracontact metric
manifolds}, Mediterr. J. Math., \textbf{11}(2014), 965--978.
- Y{\i}lmaz, H., {\em On almost pseudo quasi conformally symmetric
manifold}, Boletinde la asociacion mathemtical Venezolan,
\textbf{21(2)}(2014), 69--85.
- Zamkovoy, S., {\em Canonical connections on paracontact manifolds},
Ann. Glob., Anal. Geom., \textbf{36}(2009), 37--60.