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Home » Issues » Archive of Issues » 2020 - 2 issue » pp. 147-157

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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
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. Blair D.E. Riemannian geometry of contact and symplectic manifolds, Boston, MA: Birkhäuser, 2010. https://doi.org/10.1007/978-0-8176-4959-3
  7. Cartan E. Riemannian geometry in an orthogonal frame, Singapore: World Scientific, 2001.
  8. 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
  9. 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.
  10. 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.
  11. 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
  12. 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
  13. Ishii Y. On conharmonic transformation, Tensor, New Ser., 1957, vol. 7, pp. 73-80. https://zbmath.org/?q=an:0079.15702
  14. 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
  15. Kirichenko V.F. Differentsial'no-geometricheskie struktury na mnogoobraziyakh (Differential-geometric structures on manifolds), Odessa: Pechatnyi Dom, 2013.
  16. 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
  17. 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
  18. 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.
  19. 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
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