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 Ricci Solitons On Nearly Cosymplectic Manifolds

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 63 - 69, 28.02.2020
https://doi.org/10.18185/erzifbed.602225

Abstract

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

References

  • 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.

Yaklaşık Kosimplektik Manifoldlar üzerinde etha-Ricci Solitonlar

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 63 - 69, 28.02.2020
https://doi.org/10.18185/erzifbed.602225

Abstract

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

References

  • 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.
There are 20 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Mustafa Yıldırım 0000-0002-7885-1492

Publication Date February 28, 2020
Published in Issue Year 2020 Volume: 13 Issue: ÖZEL SAYI I

Cite

APA Yıldırım, M. (2020). Yaklaşık Kosimplektik Manifoldlar üzerinde etha-Ricci Solitonlar. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 63-69. https://doi.org/10.18185/erzifbed.602225