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Dergiler / Journal of Engineering Technology and Applied Sciences / 2019 / Cilt: 4 Sayı: 3

Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection

Gülhan Ayar
Dilek Demirhan(KARAMANOGLU MEHMETBEY UNIVERSITY)
Sayfa
131–140
Yayın Tarihi
2019-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also final part of the present paper, we study Ricci solitons on quasi-projectively flat nearly Kenmotsu manifolds with semi-symmetric metric connection.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we give some basic informations about Ricci solitons on a nearly Kenmotsu manifold and some structures on this manifolds satisfying semi-symmetric metric connection.
📊
Temel Bulgular & Veri:And then we consider some important results and theorems of Ricci solitons on Ricci-recurrent and Φ-recurrent nearly Kenmotsu manifolds with semi-symmetric metric connection.
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Sonuç & Katkı:Also final part of the present paper, we study Ricci solitons on quasi-projectively flat nearly Kenmotsu manifolds with semi-symmetric metric connection.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nearly Kenmotsu manifold · Ricci soliton · Semi-symmetric metric connection

Abstract

In this work, we give some basic informations about Ricci solitons on a nearly Kenmotsu manifold and some structures on this manifolds satisfying semi-symmetric metric connection. And then we consider some important results and theorems of Ricci solitons on Ricci-recurrent and Φ-recurrent nearly Kenmotsu manifolds with semi-symmetric metric connection. Also final part of the present paper, we study Ricci solitons on quasi-projectively flat nearly Kenmotsu manifolds with semi-symmetric metric connection.

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Bu Makaleye Atıf Yap

Ayar, G., Demirhan, D. (2019). Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. Journal of Engineering Technology and Applied Sciences, Cilt: 4 Sayı: 3, 131–140. https://doi.org/10.30931/jetas.643643

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Kaynakça (27)

  1. Bejan, C.L., Crasmareanu, M., “Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry”, Ann. Glob. Anal. Geom. (2014), doi:10. 1007/s10455-014-9414-4. Hamilton, R.S., “Three manifolds with positive Ricci curvature”, Journal of Differential Geometry 17 (2) (1982): 225-306.
  2. Hamilton, R.S., “The Ricci flow on surfaces”, Contemporary Mathematics 71 (1988): 237-261.
  3. Hamilton, R.S., “The Ricci flow on surfaces. In: Mathematics and general relativity (Santa Cruz, CA, 1986)”, Contemp. Math. Amr. Math. Soc., Providence 71 (1988): 237-262.
  4. Nagaraja, H.G., Venu, K., “Ricci Solitons in Kenmotsu Manifold”, Journal of Informatics and Mathematical Sciences 8 (2016): 29.
  5. Oztürk, H., “On α−Kenmotsu manifolds satisfying semi-symmetric conditions”, Konuralp Journal of Mathematics 5 (2017): 192-193.
  6. Kenmotsu, K., “A class of contact Riemannian manifold”, Tohoko Math. J. 24 (1972): 93-103.
  7. Nomizu, K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tohoko Mat. J. 20 (1968): 46-69.
  8. Blair, D.E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin.
  9. Shukla, A., “Nearly trans-Sasakian manifolds”, Kuwait J. Sci. Eng. 23 (2) (1996): 139–144.
  10. Küpeli Erken, I., Piotr D., Murathan, C., “On the existence of proper nearly Kenmotsu manifolds”, Mediterr. J. Math. 13 (2016): 4497-4507.
  11. Prasad, R., Kumar, S., Gautam, U.K., “On nearly Kenmotsu manifolds with semi-symmetric metric connection”, Ganita 68 (1) (2018): 133.
  12. De, U.C., “On ϕ−recurrent Kenmotsu manifolds”, Turk J. Math. 33 (2009): 17-25.
  13. Ayar, G., Yıldırım, M., “η-Ricci solitons on nearly Kenmotsu manifolds”, Asian-European Journal of Mathematics 12 (6) (2019): 2040002.
  14. Ayar, G., Yıldırım M., “Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds”, Facta Universitatis (NIS) Ser. Math. Inform. 34 (3) (2019): 503-510.
  15. Bejan, C.L., Crasmareanu, M., “Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry”, Ann. Glob. Anal. Geom. (2014), doi:10. 1007/s10455-014-9414-4. Hamilton, R.S., “Three manifolds with positive Ricci curvature”, Journal of Differential Geometry 17 (2) (1982): 225-306.
  16. Hamilton, R.S., “The Ricci flow on surfaces”, Contemporary Mathematics 71 (1988): 237-261.
  17. Hamilton, R.S., “The Ricci flow on surfaces. In: Mathematics and general relativity (Santa Cruz, CA, 1986)”, Contemp. Math. Amr. Math. Soc., Providence 71 (1988): 237-262.
  18. Nagaraja, H.G., Venu, K., “Ricci Solitons in Kenmotsu Manifold”, Journal of Informatics and Mathematical Sciences 8 (2016): 29.
  19. Oztürk, H., “On α−Kenmotsu manifolds satisfying semi-symmetric conditions”, Konuralp Journal of Mathematics 5 (2017): 192-193.
  20. Kenmotsu, K., “A class of contact Riemannian manifold”, Tohoko Math. J. 24 (1972): 93-103.
  21. Nomizu, K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tohoko Mat. J. 20 (1968): 46-69.
  22. Shukla, A., “Nearly trans-Sasakian manifolds”, Kuwait J. Sci. Eng. 23 (2) (1996): 139–144.
  23. Küpeli Erken, I., Piotr D., Murathan, C., “On the existence of proper nearly Kenmotsu manifolds”, Mediterr. J. Math. 13 (2016): 4497-4507.
  24. Prasad, R., Kumar, S., Gautam, U.K., “On nearly Kenmotsu manifolds with semi-symmetric metric connection”, Ganita 68 (1) (2018): 133.
  25. De, U.C., “On ϕ−recurrent Kenmotsu manifolds”, Turk J. Math. 33 (2009): 17-25.
  26. Ayar, G., Yıldırım, M., “η-Ricci solitons on nearly Kenmotsu manifolds”, Asian-European Journal of Mathematics 12 (6) (2019): 2040002.
  27. Ayar, G., Yıldırım M., “Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds”, Facta Universitatis (NIS) Ser. Math. Inform. 34 (3) (2019): 503-510.