SOME RESULTS ON GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS

Sourav Makhal

DOI Number
https://doi.org/10.22190/FUMI1803401M
First page
401
Last page
408

Abstract


The object of this paper is to study Codazzi type of Ricci tensor in generalized $(k,\mu )$-paracontact metric manifolds. Next we study cyclic parallel Ricci tensor in generalized $(k,\mu )$-paracontact metric manifolds. Further, we characterized generalized $(k,\mu )$-paracontact metric manifolds whose structure tensor $\phi$ is $\eta$-parallel. Finally, we investigate locally $\phi$-Ricci symmetric generalized $(k,\mu )$-paracontact metric manifolds.

Keywords

Generalized $(k,\mu )$-paracontact metric manifold, Codazzi type of tensor, cyclic parallel Ricci tensor, $\eta$-parallel $\phi$-tensor, locally $\phi$-Ricci symmetric.

Keywords


Generalized $(k,\mu)$-paracontact metric manifold, Codazzi type of tensor, cyclic parallel Ricci tensor, $\eta$-parallel $\phi$-tensor, locally $\phi$-Ricci symmetric.

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References


bibitem{blair} Blair, D.E., textit{Riemannian Geometry of contact and symlectic manifolds,} Birkhauser, Boston, (2002)

bibitem{bk} Blair, D.E., Koufogiorgos, T. and Papatoniou, B.J., textit{Contact metric manifolds satisfying a nullity condition,} Israel J. Math., {bf91}(1995), 189-214.

bibitem{boc} Boeckx, E., Cho, J. T., textit{$eta$-parallel contact metric spaces,} Diff. Geom. Appl., {bf 22}(2005), 275-285.

bibitem{cg} Calvaruso, G., textit{Homogeneous paracontact metric three-manifolds,} Illinois J. Math., {bf55}(2011), 697--718.

bibitem{ck} Capplelletti-Montano, B., Kupeli Erken, I nad Murathan, C., textit{Nullity conditions in paracontact geometry,} Diff. Geom. Appl. {bf 30}(2012), 665-693.

bibitem{ua} De, U. C., and Sarkar, A., textit{On $phi$-Ricci symmetric Sasakian manifolds,} Proceedings of the jangjeon mathematical society, {bf11}(2008), 47-52.

bibitem{gra} Gray, A. textit{Einstein-like manifild which are not Einstein,} Geom.Dedicata.,{bf7}(1974), 259-280.

bibitem{jkk} Jun, J.-B. and Kim, U.-K., textit{On $3$-dimensional almost contact metric manifolds,} Kyungpook Math. J., {bf34}(1994), 293-301.

bibitem{ke15} Kupeli Erken, I., textit{Generalized $(tilde kneq-1,tildemu)$-paracontact metric manifolds with $xi(tildemu)=0,$} Int. Electron. J. Geom., {bf8}(2015), 77-93.

bibitem{kem} Kupeli Erken, I. and Murathan, C., textit{A complete study of three-dimensional paracontact $(k,mu,nu)$-spaces,} arXiv: 1305.1511.

bibitem{kw} Kaneyuki, S. and Williams, F.L, textit{Almost paracontact and parahodge structure on manifolds,} Nagoya Math. J. {bf 99}(1985), 173-187.

bibitem{martin} Martin-Molina, V., textit{Paracontact metric manifolds without a contact metric counterpart,} Taiwanese J. Math., {bf19}(2015), 175-191.

bibitem{sz} Szab'{o}, Z. I., textit{Structure theorems on Riemannian spaces satisfying $R(X,Y)cdot R=0$ I the local version,} J. Diff. Geom. {bf17}(1982), 531-582.

bibitem{y} Yano, K., textit{Concircular geometry I. Concircular transformations,} P. Imp. Acad. {bf36}(1940), 195-200.

bibitem{yb} Yano, K. and Bochner, S., textit{Curvature and Betti numbers,} Ann. Math. Stud. {bf32}(1953).

bibitem{zs} Zamkovoy, S., textit{Canonical connection on paracontact manifolds,} Ann. Global Anal. Geom. {bf36}(2009), 37-60.




DOI: https://doi.org/10.22190/FUMI1803401M

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