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

Year 2020, , 167 - 172, 23.12.2020
https://doi.org/10.32323/ujma.799576

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.

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.
Year 2020, , 167 - 172, 23.12.2020
https://doi.org/10.32323/ujma.799576

Abstract

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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İnan Ünal

Publication Date December 23, 2020
Submission Date September 24, 2020
Acceptance Date November 2, 2020
Published in Issue Year 2020

Cite

APA Ünal, İ. (2020). On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection. Universal Journal of Mathematics and Applications, 3(4), 167-172. https://doi.org/10.32323/ujma.799576
AMA Ünal İ. On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection. Univ. J. Math. Appl. December 2020;3(4):167-172. doi:10.32323/ujma.799576
Chicago Ünal, İnan. “On Submanifolds of $N(k)$-Quasi Einstein Manifolds With a Type of Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications 3, no. 4 (December 2020): 167-72. https://doi.org/10.32323/ujma.799576.
EndNote Ünal İ (December 1, 2020) On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection. Universal Journal of Mathematics and Applications 3 4 167–172.
IEEE İ. Ünal, “On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection”, Univ. J. Math. Appl., vol. 3, no. 4, pp. 167–172, 2020, doi: 10.32323/ujma.799576.
ISNAD Ünal, İnan. “On Submanifolds of $N(k)$-Quasi Einstein Manifolds With a Type of Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications 3/4 (December 2020), 167-172. https://doi.org/10.32323/ujma.799576.
JAMA Ünal İ. On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection. Univ. J. Math. Appl. 2020;3:167–172.
MLA Ünal, İnan. “On Submanifolds of $N(k)$-Quasi Einstein Manifolds With a Type of Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications, vol. 3, no. 4, 2020, pp. 167-72, doi:10.32323/ujma.799576.
Vancouver Ünal İ. On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection. Univ. J. Math. Appl. 2020;3(4):167-72.

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