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## Archive of Issues

Iraq Basrah
Year
2020
Volume
30
Issue
2
Pages
147-157
 Section Mathematics Title Quaisi invariant conharmonic tensor of special classes of locally conformal almost cosymplectic manifold Author(-s) Al-Hussaini F.H.a, Abood H.M.a Affiliations University of Basraha Abstract The authors classified a locally conformal almost cosympleсtic manifold ($\mathcal{LCAC_{S}}$-manifold) according to the conharmonic curvature tensor. In particular, they have determined the necessary conditions for a conharmonic curvature tensor on the $\mathcal{LCAC_{S}}$-manifold of classes $CT_{i}, i=1,2,3$ to be $\Phi$-quaisi invariant. Moreover, it has been proved that any $\mathcal{LCAC_{S}}$-manifold of the class $CT_{1}$ is conharmoniclly $\Phi$-paracontact. Keywords locally conformal almost cosymplectic manifold, conharmonic curvature tensor, $\Phi$-quaisi invariant, conharmonically $\Phi$-paracontact UDC 514.7 MSC 53C55, 53B35 DOI 10.35634/vm200201 Received 12 February 2020 Language English Citation Al-Hussaini F.H., Abood H.M. Quaisi invariant conharmonic tensor of special classes of locally conformal almost cosymplectic manifold, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 2, pp. 147-157. References Abood H.M., Al-Hussaini F.H. Locally conformal almost cosymplectic manifold of $\Phi$-holomorphic sectional conharmonic curvature tensor, European Journal of Pure and Applied Mathematics, 2018, vol. 11, no. 3, pp. 671-681. https://doi.org/10.29020/nybg.ejpam.v11i3.3261 Abood H.M., Al-Hussaini F.H. Constant curvature of a locally conformal almost cosymplectic manifold, AIP Conference Proceedings, 2019, vol. 2086, issue 1, 030003. https://doi.org/10.1063/1.5095088 Abood H.M., Al-Hussaini F.H. On the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold, Communications of the Korean Mathematical Society, 2020, vol. 35, no. 1, pp. 269-278. https://doi.org/10.4134/CKMS.c190003 Asghari N., Taleshian A. On the conharmonic curvature tensor of Kenmotsu manifolds, Thai Journal of Mathematics, 2014, vol. 12, no. 3, pp. 525-536. http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/410 Blair D.E. The theory of quasi-Sasakian structures, Journal of Differential Geometry, 1967, vol. 1, no. 3-4, pp. 331-345. https://doi.org/10.4310/jdg/1214428097 Blair D.E. Riemannian geometry of contact and symplectic manifolds, Boston, MA: Birkhäuser, 2010. https://doi.org/10.1007/978-0-8176-4959-3 Cartan E. Riemannian geometry in an orthogonal frame, Singapore: World Scientific, 2001. Chanyal S.K., Upreti J. Conharmonic curvature tensor on $(\kappa,\mu)$-contact metric manifold, An. Științ. Univ. Al. I. Cuza Iași Mat. (N.S.), 2016, vol. 2, issue F2, pp. 681-694. https://www.math.uaic.ro/~annalsmath/new/?page_id=351 Chinea D., Marrero J.C. Classification of almost contact metric structures, Revue Roumaine de Mathématiques Pures et Appliquées, 1992, vol. 37, no. 3, pp. 199-211. Dwivedi M.K., Kim J.-S. On conharmonic curvature tensor in $K$-contact and Sasakian manifolds, Bulletin of the Malaysian Mathematical Sciences Society. Second Series, 2011, vol. 34, no. 1, pp. 171-180. Ghosh S., De U.C., Taleshian A. Conharmonic curvature tensor on $N(K)$-contact metric manifolds, ISRN Geometry, 2011, vol. 2011, article ID 423798, 11 p. https://doi.org/10.5402/2011/423798 Goldberg S.I., Yano K. Integrabilty of almost cosymplectic structures, Pacific Journal of Mathematics, 1969, vol. 31, no. 2, pp. 373-382. https://doi.org/10.2140/pjm.1969.31.373 Ishii Y. On conharmonic transformation, Tensor, New Ser., 1957, vol. 7, pp. 73-80. https://zbmath.org/?q=an:0079.15702 Kharitonova S.V. On the geometry of locally conformal almost cosymplectic manifolds, Mathematical Notes, 2009, vol. 86, no. 1, pp. 121-131. https://doi.org/10.1134/S0001434609070116 Kirichenko V.F. Differentsial'no-geometricheskie struktury na mnogoobraziyakh (Differential-geometric structures on manifolds), Odessa: Pechatnyi Dom, 2013. Kirichenko V.F., Rustanov A.R. Differential geometry of quasi Sasakian manifolds, Sbornik: Mathematics, 2002, vol. 193, no. 8, pp. 1173-1201. https://doi.org/10.1070/SM2002v193n08ABEH000675 Olszak Z. Locally conformal almost cosymplectic manifolds, Colloquium Mathematicum, 1989, vol. 57, no. 1, pp. 73-87. https://doi.org/10.4064/cm-57-1-73-87 Taleshian A., Prakasha D.G., Vikas K., Asghari N. On the conharmonic curvature tensor of $LP$-Sasakian manifolds, Palestine Journal of Mathematics, 2016, vol. 5, no. 1, pp. 177-184. Volkova E.S. Curvature identities of normal manifolds of Killing type, Mathematical Notes, 1997, vol. 62, no. 3, pp. 296-305. https://doi.org/10.1007/BF02360870 Full text