RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON NEARLY COSYMPLECTIC MANIFOLDS

Öz

In this article, a number of properties have been obtained by examining Ricci solitons and gradient Ricci solitons on nearly cosymplectic manifolds.

Anahtar Kelimeler

• Ricci soliton
• gradient Ricci soliton
• nearly cosymplectic manifold

Kaynakça

1. Adile, D., Aktan, N.: Some results on Nearly cosymplectic manifolds, Universal Journal of Mathematics and Applications, 2(2019), 218-223.
2. Ayar, G., Tekin, P., Aktan, N., : Some Curvature Conditions on Nearly Cosymplectic Manifolds, Indian Journal Of Industrial and Applied Mathematics, 10(2019), 51-58.
3. Ayar, G., Yıldırım, M. : Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds, Facta Universitatis(Nis) Ser. Math. Inform., 34(2019), 503-510.
4. Ayar, G., Yıldırım, M.: etha-Ricci solitons on Nearly Kenmotsu Manifolds, Asian-European Journal of Mathematics, 12(2019), 2040002-2040010.
5. Barua, B., De, U. C.: Characterizations of a Riemannian manifold admitting Ricci solitons. Facta Universitatis(NIS)Ser. Math. Inform., 28(2013), 127-132.
6. Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics,Springer-Verlag, Berlin, 1976.
7. Blair, D. E. Almost Contact Manifolds with Killing Structure Tensors, I. Pac. J. Math. 39 (1971), 285-292.
8. Blair, D. E., Goldberg S.I. Topology of almost contact manifolds, J.Differential Geometry 1(1967), 347-354.

9. Catino, G., Mazzieri, L. Gradient Einstein solitons, Nonlinear Anal. 132(2016), 66-94.
10. Chave, T., Valent, G.: Quasi-Einstein metrics and their renormalizability properties. Helv. Phys. Acta. 69(1996), 344-347.
11. Chen, B.Y., Geometry of submanifolds, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1973.
12. Chinea, D., de Leon M., Marrero J. C.: Topology of cosymplectic manifolds, J. Math. Pures Appl., 72 (1993), 567-591.
13. Chow, B., Knopf, D., The Ricci flow: An introduction, Mathematical Surveys and Monographs 110. American Math. Soc., 2004.
14. De, U. C. Ricci soliton and gradient Ricci soliton on P-Sasakian manifolds. The Aligarh Bull. of Maths., 29(2010), 29-34.
15. De Nicola, A., Dileo, G., Yudin, I. On Nearly Sasakian and Nearly Cosymplectic Manifolds, Annali di Matematica , 197(2018), 127-138.
16. Endo, H. On the Curvature Tensor of Nearly Cosymplectic Manifolds of Constant phi-sectional curvature. An. Stiit. Univ. "Al. I. Cuza" Iasi. Mat. (N.S.), (2005), 439-454.
17. Friedan, D. Non linear models in 2 + epsilon dimensions. Ann. Phys. 163(1985), 318419.
18. Gray, A., Nearly Kahler Manifolds, J. Differential Geom. 4 (1970), 283-309.
19. Hamilton, R. S. Three-manifolds with positive Ricci curvature, Journal of Differential Geometry, 17(1982), 255-306.
20. Hamilton, R. S.: The Ricci flow on surfaces. Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., American Math. Soc.,71(1988),237-262.
21. Ivey, T.: Ricci solitons on compact 3-manifolds. Differential Geo. Appl. 3(1993), 301-307.
22. Libermann, P.: Sur les automorphismes innit esimaux des structures symplectiques et de atructures de contact, oll. G'eom. Diff. Globale, (1959), 37-59.
23. Mukut Mani Tripathi, Ricci solitons in contact metric manifolds, arXiv:0801.4222 (or arXiv:0801.4222v1 [math.DG] for this version)
24. Perelman, G., The entopy formula for the Ricci ow and its geometric applications, http://arxiv.org/abs/math.DG/02111159.
25. Sharma, R.: Certain results on K-contact and (k; m)-contact manifolds. Journal of Geometry, 89(2008), 138-147
26. Yıldırım, M., Ayar, G.: Nearly cosymplectic manifolds with nullity conditions, Asian-Europan journal of Mathematics, 12(2019), 2040012-2040021.