On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection

Year 2020, Volume: 3 Issue: 4, 167 - 172, 23.12.2020

İnan Ünal

https://doi.org/10.32323/ujma.799576

Cited By: 2

Abstract

In this study, we consider the $ N(k)- $quasi Einstein manifolds with respect to a type of semi-symmetric metric connection. We suppose that the generator of $ N(k)- $quasi-Einstein manifolds is parallel with respect to semi-symmetric metric connection and we classify such manifolds. In addition, we consider the submanifolds of a $ N(k)- $quasi Einstein manifold and we obtain some conditions on the totally geodesic and the totally umbilic submanifolds. Finally, we consider a para-Kenmotsu space form as an example of $ N(k)- $quasi-Einstein manifolds.

Keywords

N(k)-quasi Einstein manifolds, Totally geodesic, Totally umbilical, Para-Kenmotsu

References

• [1] K. Yano, M. Kon, Structures on Manifolds, Series in Pure Mathematics, World Scientific, 3, 1984.
• [2] C. Ozgur , M. M. Tripathi, On the concircular curvature tensor of an N(k)-quasi Einstein manifold, Math. Pannon., 18(1), (2007), 95-100.
• [3] C. Ozgur, N(k)-quasi Einstein manifolds satisfying certain conditions, Chaos Solitons Fractals, 38(5) (2008), 1373-1377.
• [4] A. Yıldız, U.C. De, A. C¸ etinkaya, On some classes of N(k)-quasi Einstein manifolds, Proc. Natl. Acad. Sci. India A, 83(3) (2013), 239-245.
• [5] M.C. Chaki, On quasi Einstein manifolds, Publ. Math. Debr., 57 (2000), 297-306.
• [6] S.K. Chaubey, Existence of N(k)-quasi Einstein manifolds, Facta universitatis Nis. Ser. Math.Inform., 32(3) (2017), 369-385.
• [7] U.C. De, G.C.Ghosh, On quasi Einstein manifolds, Period. Math. Hung., 48 (2004), 223-231.
• [8] U. C. De, S. Shenawy, Generalized quasi-Einstein GRW space-times, Int. J. Geom. Methods Mod. Phys., 16(08) (2019), 1950124.
• [9] G.C. Ghosh, U.C. De, T.Q. Binh, Certain curvature restrictions on a quasi Einstein manifolds, Publ. Math. Debr. 69 (2006), 209-217.
• [10] A.T. Kotamkar, A. Tarini, T. Brajendra, Certain curvature conditions catisfied by N(k)-quasi Einstein manifolds, Int. J. Innov. Res. Adv. Eng. G. , 1(9) (2015), 1-9.
• [11] C. Murathan, C. Ozgur, Riemannian manifolds with a semi-symmetric metric connection satisfying some semi-symmetry conditions, Proc. Est. Acad. Sci., 57(4) (2008), 210–216.
• [12] H.G. Nagaraja, K. Venu, On Ricci solitons in N(k)-quasi Einstein manifolds, NTMSCI, 5(3) (2017), 46-52.
• [13] G. Pitis¸, Geometry of Kenmotsu Manifolds, Editura Universitatii Transilvania, 2007.
• [14] B.B. Sinha, K. L. Sai Prasad, A class of almost para contact metric manifolds, Bull. Cal. Math. Soc., 87 (1995), 307–312.
• [15] M.M. Tripathi, J. Kim, On N(k)􀀀quasi Einstein manifolds, Commun. Korean Math. Soc., 22 (2007), 411-417.
• [16] A. Taleshian, A. A. Hosseinzadeh, Investigation of some conditions on N(k)-quasi Einstein manifolds, Bull. Malaysian Math. Sci. Soc, 34(3) (2011), 455-464.
• [17] K. Yano, On semi-symmetric connection, Revue Roumaine Math. Pures Appl., 15 (1970), 1570-1586.
• [18] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(1) (2008), 37–60.