Asian Journal of Mathematics and Computer Research

Study of a Projective Ricci Semi-symmetric Nearly Kaehler Manifold

Asian Journal of Mathematics and Computer Research, Volume 30, Issue 3, Page 19-29
DOI: 10.56557/ajomcor/2023/v30i38324

Abstract


We inaugurate a new curvature properties of projective curvature tensor in nearly Kaehler manifold. We defined projective Ricci semi-symmetric quasi-Einstein nearly Kaehler manifold, Projective Ricci semisymmetric generalised quasi-Einstein nearly Kaehler manifold and a Projective Ricci semi-symmetric pseudo generalised quasi-Einstein nearly Kaehler manifold and also found some results in the manifold.

Keywords:
  • Nearly Kaehler manifold
  • Einstein manifold
  • quasi-Einstein manifold
  • generalised quasi-Einstein manifold
  • pseudo generalised quasi-Einstein manifold
  • projective curvature tensor

How to Cite

Chaturvedi, B. B., & Kaushik, K. B. (2023). Study of a Projective Ricci Semi-symmetric Nearly Kaehler Manifold. Asian Journal of Mathematics and Computer Research, 30(3), 19–29. https://doi.org/10.56557/ajomcor/2023/v30i38324

References

Chaki MC, Maity RK. On quasi-Einstein manifolds, Publ. Math. Debrecen. 2000;57:297-306.

De UC, Ghose GC. On quasi-Einstein and special quasi-Einstein manifolds, Proc.of the Conf. of Mathematics and its applications. Kuwait University. 2004;178-191.

O zgur C. N(k)-quasi-Einstein manifold satisfying certain conditions, Chaos Solitons Fractals. 2008;38:1373- 1377.

Debnath P, Konar A. On quasi-Einstein manifolds and quasi-Einstein spacetime, Di er. Geom. Dyn. Syst. 2010;12:73-82.

Guha S. On quasi-Einstein and generalised quasi-Einstein manifolds, Facta Univ. Ser. Autom. Control Robot. 2003;3:821-842.

Chaki MC. On generalized quasi-Einstein manifolds, Publ. Math. Debrecen. 2001;58:683-691.

De UC, Ghosh GC. On generalised quasi-Einstein manifolds, Kyungpook Math. J. 2004;44:607-615.

O zgur C. On some classes of super quasi-Einstein manifolds, Chaos Solitons Fractals. 2009;40:1156-1161.

O zgur C, Sular S. On N(k)-quasi-Einstein manifolds satisfying certain conditions, Balkan J. Geom. Appl. 2008;13:74-79.

Taleshian A, Hosseinzadeh AA. Investigation of some conditions on N(k)-quasi Einstein manifolds, Bull. Malays. Math. Sci. Soc. 2011;34:455-464.

Tripathi MM, Kim JS. On N(k)-quasi-Einstein manifolds, Commun. Korean Math. Soc., 2007;22(3):411- 417.

Hosseinzadeh A, Taleshian A. On conformal and quasi-conformal curvature tensor of N(k)-quasi-Einstein manifold. Commun. Korean Math. Soc. 2012;27:317-326.

Nagaraja HG. On N(k)-mixed quasi-Einstein manifolds, Eur. J. Pure Appl. Math. 2010;3:16-25.

Jawarneh M, Tashtoush M. On Generalized semi-pseudo Ricci symmetric manifold, In International Mathematical Forum. 2012;7(6):297-303.

Jawarneh M, Tashtoush M. M{Projective Curvature Tensor on Kaehlar Manifold, International Journal of Contemporary Mathematical Sciences. 2011;6(33):1607-1617.

De UC, Gazi AK. On nearly quasi-Einstein manifolds, NoviSad J. Math. 2008;38:531-582.

Shaikh AA, Jana SK. On pseudo generalised quasi Einstein manifold, Tamkang Journal of Mathematics. 2008;39(1):9-24.

Hui SK, Lemence RS. On generalized quasi Einstein manifold admitting W2-curvature tensor, Int. Journal of Math. Analysis. 2012;6(23):1115 - 1121.

Prakasha DG, Venkatesha H. Some results on generalised quasi-Einstein manifolds, Chinese Journal of Mathematics (Hindawi Publishing Corporation); 2014.

Walker AG. On Ruse`s spaces of recurrent curvature. Proc. London Math. Soc. 1950;52:36-64.

Adati T, Miyazawa T. On a Riemannian space with recurrent conformal curvature. Tensor N. S. 1967;18:348- 354.

Szabo ZI. Structure theorems on Riemannian spaces satisfying R(X,Y).R=0. the local version. J. Di . Geom. 1982;17:531-582.

Defever F. Ricci-semisymmetric hypersurfaces, Balkan Journal of Geometry and its appl. 2000;5:81-91.

Chaturvedi BB, Gupta BK. On Bochner Ricci semi-symmetric Hermitian manifold, Acta Math. Univ. Comenianae. 2018;LXXXVII(1)25-34.

Chaturvedi BB, Gupta BK. On Ricci pseudo-symmetric mixed generalised quasi-Einstein Hermitian manifolds, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. DOI-https://doi.org/10.1007/s40010-020-00728- 3.

Chaturvedi BB, Gupta BK. On Bochner Ricci pseudo-symmetric Hermitian manifolds, Southeast Asian Bulletin of Mathematics. 2020;44:479-490.

Chaturvedi BB, Kunj Bihari Kaushik. On Ricci pseudo-symmetric super quasi-Einstein nearly Kaehler manifold, Palestine Journal of Mathematics. 2023;12(1):892-899.

Chaturvedi BB, Gupta BK, Mehraj Ahmad Lone. On Ricci semi-symmetric mixed super quasi-Einstein nearly kaehler manifold, J. Int. Acad. Phys. Sci. 2022;26(1):17-27.

Mishra RS. Structures On a di erentiable manifold and their applications, Chandrama Prakashan Allahabad; 1984.

  • 0 times
    PDF Download: 0 times

Download Statistics

Downloads

Download data is not yet available.

Current Issue

Subscription

Login to access subscriber-only resources.

Information