Some Results on $\mathcal{W}_8$-Curvature Tensor in $\alpha$-Cosymplectic Manifolds

Year 2022, Volume: 10 Issue: 4, 208 - 216, 22.12.2022

Selahattin Beyendi

Abstract

The object of this paper is to study W8 curvature tensors in alpha-cosymplectic
manifolds.

Keywords

$\mathcal{W}_{8}$-curvature tensor , $\alpha$-cosymplectic manifold , $\eta$-Ricci soliton

Supporting Institution

-

Project Number

-

Thanks

-

References

• [1] Aktan,N.,Yıldırım,M.,Murathan,C.: Almostf-cosymplecticmanifolds.Mediterr.J.Math.11(2),775-787(2014).
• [2] Amruthalakshmi, M. R., Prakasha, D. G., Turki, N. B. and Unal, I.: η-Ricci tensor on α-cosymplectic manifolds, Hindawi Adv. Math. Phys., Vol. Article ID 7939654, 11 pag., (2022).
• [3] Beyendi, S., Ayar, G., Aktan, N.: On a type of α-cosymplectic manifolds, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68, 852-861 (2019).
• [4] Beyendi, S., Yıldırım, M.: On generalized weakly symmetric α-cosymplectic manifolds , Hacet. J. Math. Stat, Vol: 50 (6) 1745-1755 (2021).
• [5] Blaga.: η-Ricci solitons on para-Kenmotsu manifolds. Balkan J. Geom. Appl. 20 (1), 1-13 (2015).
• [6] Blair,D.E.:ContactmanifoldsinRiemanniangeometry,LectureNotesinMath.509,Springer-Verlag,Berlin,(1976).
• [7] Chen, X.: Notes on Ricci solitons in f-cosymplectic manifolds, J. Math. Phys. Anal. Geom., Vol: 13, No. 3, pp., 242-253 (2017).
• [8] Deszcz, R.: On Ricci-pseudosymmetric warped products, Demonstratio Math., 22, 1053-1065 (1989).
• [9] Deszcz, R.: On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44, 1-34 (1992).
• [10] Erken, I. K.: On a classification of almost α-cosymplectic manifolds, Khayyam J. Math., 5, 1-10 (2019).
• [11] Goldberg, S. I. and Yano, K.: Integrability of almost cosymplectic structure, Pac. J. Math. 31 373-381 (1969).
• [12] Hui,S.K.andLemence,R.S.:Riccipseudosymmetricgeneralizedquasi-Einsteinmanifolds,SUT.J.Math.,51,195-213 (2015).
• [13] Ingalahalli, G. Anil, S. C., Begewadi, C. S.: A study on W8-curvature tensor in Kenmotsu manifolds, Int. J. Math. And Appl., 8 (2), 27-34 (2020).
• [14] Jahanara, B., Haesen, S., Senturk, Z. and Verstraelen, L.: On the parallel transport of the Ricci curvatures, J. Geom. Phys., 57, 1771-1777 (2007).
• [15] Kenmotsu,K.: AclassofalmostcontactRiemannianmanifolds.TohokuMath.J.24(1),93-103(1972).
• [16] Kim, T. W., Pak, H. K.: Canonical foliations of certain classes of almost contact metric structures, Acta Math, Sinica, Eng. Ser. Aug., 21 (4), 841-846 (2005).
• [17] Li, J. and Liu, X.: Ricci solitons on homogeneous almost α-cosymplectic three-manifolds, Mediterr. J. Math., https://doi.org/10.1007/s00009-021-01947-7 1660-5446/22/010001-12, 19:26, (2022).
• [18] Matsumoto, K., Ianus, S. and Milrai, I.: Publicationes Mathematicae Debrecen, 33(3-4), 199-204 (1986).
• [19] Njori, P. W., Moindi, S. K. and Pokhariyal, G. P.: A study on W6-curvature tensors and W8-curvature tensors in Kenmotsu manifolds admitting semisymmetric metric connection, Int. J. Stat. Appl. Math., 6 (2), 01-05 (2021).
• [20] Olszak, Z.: On almost cosymplectic manifolds, Kodai Math, 4 (2), 239- 250 (1981).
• [21] Öztürk, H., Murathan, C., Aktan, N., Vanlı, A. T.: Almost α-cosymplectic f-manifolds, Analele stııntıfıce ale unıversıtatıı ’AI. I. Cuza’ Dı ıas ̧ı S. N., Matematica, Tomul LX, f. 1., (2014).
• [22] Pokhariyal, G. P.: Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci., 5 No. 1, 133-139 (1982).
• [23] Pokhariyal, G. P., Mishra, R. S.: The curvature tensor and their relativistic significance, Yokohoma Math. J. 18, 105-108 (1970).
• [24] Shaikh, A. A. and Hui, S. K.: On locally φ-symmetric β-Kenmotsu manifolds, Extracta Mathematicae, 24, 301-316 (2009).
• [25] Tripathi, M. M. and Gupta, P.: T-curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies, Vol: 4, No: 1, 117-129 (2011).
• [26] Uwimbabazi Ruganzu, L. F., Moindi, S. K., Pokhariyal, G. P. and Katende, J.: η-Ricci solitons defined with W8-curvature tensor and cylic Ricci tensor on para-Kenmotsu manifolds, Int. J. Stat. Appl. Math., 4 (5), 80-84 (2019).
• [27] Wanjiru, W. K.: A study of W6-curvature tensor in sasakian manifold, (IJRSI), Vol: 6 (5), 343-346 (2019).
• [28] Yıldırım,M.,Ayar,G.:RiccisolitonsandgradientRiccisolitonsonnearlycosymplecticmanifolds,JournalofUniversal Math., 4 (2) 201-208 (2021).
• [29] Yıldız, A., De, U. C.: On a type of Kenmotsu manifolds, Differential Geometry- Dynamical Systems, Vol: 12, 289-298 (2010).
• [30] Yoldas,H.I.: Someresultsonα-cosymplecticmanifoldsBull.Transilv.Univ.Bra.,Vol:1(63),No.2,115-128(2021). .