 Ricci Solitons On Nearly Cosymplectic Manifolds

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 63 - 69, 28.02.2020

Mustafa Yıldırım

https://doi.org/10.18185/erzifbed.602225

Öz

The object of the present paper is to examine 𝜂 −Ricci solitons on nearly cosymplectic manifolds and

investigate curvature conditions for which 𝜂 −Ricci solitons in nearly cosymplectic manifolds

Anahtar Kelimeler

Nearly cosymplectic manifolds, 𝜂 −Ricci solitons, Ricci-semisymmetric manifolds, Einsteinsemmisymetric manifolds

Yaklaşık Kosimplektik Manifoldlar üzerinde etha-Ricci Solitonlar

Öz

Bu çalışmanın amacı yaklaşık kosimplektik
manifoldlar üzerinde  Ricci solitonlar ele
alınarak bazı eğrilik koşulları altında bu tür manifoldların yapısını
incelemektir. 

Anahtar Kelimeler

Yaklaşık kosimplektik manifoldlar, η-Ricci solitonlar, Ricci yarı-simetrik manifoldlar, Einstein yarı-simetrik manifoldlar.

Kaynakça

• Blair, D.E. 1972. “Almost Contact Manifolds with Killing Structure Tensors I”, Pacific Journal of Mathematics, 39(2), 285-292.
• Blair, D.E. & and Showers, D.K. 1974. “Almost Contact Manifolds with Killing Structures Tensors II’’, Journal of Differential Geometry, 9(4), 577-582.
• Endo, H. 2005. ‘‘On the Curvature Tensor of Nearly Cosymplectic Manifolds of Constant φ-sectional curvature’’, An. Stiit. Univ. "Al. I. Cuza" Iasi. Mat. (N.S.), 439-454.
• Banaru, M. 2002. ‘‘On nearly cosymplectic hyper-surfaces in nearly-Kahlerian Manifolds’’, Studia Univ. Babes-Bolyai. Math. Cluj-Napoca, 47(3), 2-11.
• De Nicola, A. & Dileo, G. & Yudin, I. 2018. ‘‘On Nearly Sasakian and Nearly Cosymplectic Manifolds’’, Annali di Matematica , (197)1, 127–138.
• Hamilton, R.S. 1982. ‘‘Three-manifolds with positive Ricci curvature’’, Journal of Differential Geometry, 17(2), 255-306.
• Hamilton, R.S. 1986. ‘‘The Ricci flow on sur-faces’’, Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., American Math. Soc., 71, 237-262.
• Perelman, G. (2002)‘’The entopy formula for the Ricci flow and its geometric applications’’, http://arUiv.org/abs/math.DG/02111159.
• Sharma, R. 2014. ‘‘Almost Ricci solitons and K-contact geometry, ’’ Monatsh. Math., 175, 621–628.
• Tripathi, M.M.,2008. ‘‘Ricci solitons in contact metric manifold,’’arUiv:0801,4222v1.
• Blaga, A.M., 2015. ‘‘ η-Ricci solitons on para-kenmotsu manifolds,’’ Balkan Journal of Geometry and Its Applications, 20, 1–13.
• Bejan, C.L. & Crasmareanu, M., 2011. ‘‘Ricci solitons in manifolds with quasi-constant curvature,’’ Publicationes Mathematicae Debrecen, 78(1), 235-243.
• Cho, J.T. & Kimura, M., 2009. ‘‘Ricci solitons and real hypersurfaces in a compleU space form’’, Tohoku Math. Journal, 61(2), 205-212.
• Calin,C. & Crasmareanu, M., 2012. ‘‘Eta-Ricci solitons on Hopf hypersurfaces in compleU space forms’’, Revue Roumaine de Mathematiques pures et appliques, 57(1), 55-63.
• Aktan, N. & Tekin, P. 2017. ‘’An introduction to the new type of Globally framed manifolds’’, AIP Conference Proceedings, 20051-20060.
• Sharma, R., B.B. Sinha, 1983. “On para-A-Einstein manifolds”, Publications De L’institut Mathematique, 34(48), 211-215.
• Ayar, G. & Tekin, P.& Aktan, N. 2019. “Some curvature conditions on nearly cosymplectic manifolds”, Indian Journal of Industrial and Applied Mathematics, 10(1), 51-58.
• Ayar, G. & Yıldırım, M. 2020. “ Ricci solitons on nearly Kenmotsu Manifolds”, Asian Europan journal of Mathematics, 13(1), 2040002 (8pages)
• Yıldırım, M. Ayar, G. & 2020. “ Nearly cosymplectic manifolds with nullity conditions”, Asian Europan journal of Mathematics, 13(1), 2040012(10pages)
• Ayar, G. & Yıldırım, M. 2019. “ Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds”, Facta Unıversitatis (NIS) Ser. Math. Inform.