On Ricci solitons in N(k) - quasi Einstein manifolds

Abstract

He object of the present paper is to study N(k)-quasi Einstein manifolds satisfying certain curvature conditions. Further we study gradient Ricci solitons on N(k)-quasi Einstein manifolds.

Keywords

• Quasi Einstein manifold,projective curvature tensor,pseudosymmetry

Kaynakça

1. A. L. Besse. Einstein manifolds, volume 10 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Springer-Verlag, Berlin, 1987.
2. M. C. Chaki. On generalized quasi Einstein manifolds. Publ. Math. Debrecen, 58(4):683-691, 2001.
3. M. C. Chaki and R. K. Maity. On quasi Einstein manifolds. Publ. Math. Debrecen, 57(3-4):297-306, 2000.
4. M. Crasmareanu. Parallel tensors and ricci solitons in n(k)- quasi einstein manifold. Indian Journal of Pure and applies Mathematics, 2012.
5. Sengupta J. De, U. C. and D. Saha. Conformally at quasi einstein spaces. Kyungpook math J., 46(3), 2006.
6. U. C. De and G. C. Ghosh. On quasi Einstein manifolds. Period. Math. Hungar., 48(1-2):223-231, 2004.
7. U. C. De and G. C. Ghosh. On conformally at special quasi Einstein manifolds. Publ. Math. Debrecen, 66(1-2):129-136, 2005.
8. U. C. De and G. C. Ghosh. On quasi Einstein and special quasi Einstein manifolds. In Proceedings of the International Conference on Mathematics and its Applications (ICMA 2004), pages 178-191. Kuwait Univ. Dep. Math. Comput. Sci., Kuwait, 2005.

9. A. Einstein. Grundzuge der relativitats theory. Springer, Berlin, 2002.
10. M. S. El Naschie. G odel universe, dualities and high energy particle ine-innity. Chaos, Solutions and Fractals, 25:759-764, 2005.
11. M. S. El Naschie. Is einsteins general eld equation more fundamental than quantum eld theory and particle physics?on quasi Einstein and special quasi Einstein manifolds. Chaos, Solutions and Fractals, 30:525-531, 2006.
12. S. Guha. On quasi Einstein and generalized quasi Einstein manifolds. Facta Univ. Ser. Mech. Automat. Control Robot., 3(14):821-842, 2003. Nonlinear mechanics, nonlinear sciences and applications, I (Nis, 2003).
13. A. Hosseinzadeh and A. Taleshian. On conformal and quasi-conformal curvature tensors of an N(k)-quasi Einstein manifold. Commun. Korean Math. Soc., 27(2):317-326, 2012.
14. M. Matsumoto and G. Chuman. On the C-Bochner curvature tensor. TRU Math., 5:21-30, 1969.
15. H. G. Nagaraja. On n(k) -quasi einstein manifold. European Journal of Pure and Applied Mathematics, 3:16-25, 2010.
16. C. Ozgur. N(k)-quasi Einstein manifolds satisfying certain conditions. Chaos Solitons Fractals, 38(5):1373-1377, 2008.
17. C. Ozgur and M. M. Tripathi. On the concircular curvature tensor of an N(k)-quasi Einstein manifold. Math. Pannon., 18(1):95-100, 2007.
18. A. Taleshian and A. A. Hosseinzadeh. Investigation of some conditions on N(k)-quasi Einstein manifolds. Bull. Malays. Math. Sci. Soc. (2), 34(3):455-464, 2011.
19. S. Tanno. Ricci curvatures of contact Riemannian manifolds. Tohoku Math. J. (2), 40(3):441-448, 1988.
20. M. M. Tripathi and J. Kim. On N(k)-quasi Einstein manifolds. Commun. Korean Math. Soc., 22(3):411-417, 2007.
21. L. Verstraelen. Comments on pseudo-symmetry in the sense of Ryszard Deszcz. pages 199-209, 1994.
22. A. Yildiz, U. C. De, and A. Cetinkaya. On some classes of N(k)-quasi Einstein manifolds. Proc. Nat. Acad. Sci. India Sect. A, 83(3):239-245,2013.