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

Year 2019, , 131 - 140, 31.12.2019
https://doi.org/10.30931/jetas.643643

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.

References

  • 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.
  • Hamilton, R.S., “The Ricci flow on surfaces”, Contemporary Mathematics 71 (1988) : 237-261.
  • 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.
  • Nagaraja, H.G., Venu, K., “Ricci Solitons in Kenmotsu Manifold”, Journal of Informatics and Mathematical Sciences 8 (2016) : 29.
  • Oztürk, H., “On α−Kenmotsu manifolds satisfying semi-symmetric conditions”, Konuralp Journal of Mathematics 5 (2017) : 192-193.
  • Kenmotsu, K., “A class of contact Riemannian manifold”, Tohoko Math. J. 24 (1972) : 93-103.
  • Nomizu, K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tohoko Mat. J. 20 (1968) : 46-69.
  • Blair, D.E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin.
  • Shukla, A., “Nearly trans-Sasakian manifolds”, Kuwait J. Sci. Eng. 23 (2) (1996) : 139–144.
  • Küpeli Erken, I., Piotr D., Murathan, C., “On the existence of proper nearly Kenmotsu manifolds”, Mediterr. J. Math. 13 (2016) : 4497-4507.
  • Prasad, R., Kumar, S., Gautam, U.K., “On nearly Kenmotsu manifolds with semi-symmetric metric connection”, Ganita 68 (1) (2018) : 133.
  • De, U.C., “On ϕ−recurrent Kenmotsu manifolds”, Turk J. Math. 33 (2009) : 17-25.
  • Ayar, G., Yıldırım, M., “η-Ricci solitons on nearly Kenmotsu manifolds”, Asian-European Journal of Mathematics 12 (6) (2019) : 2040002.
  • 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.
Year 2019, , 131 - 140, 31.12.2019
https://doi.org/10.30931/jetas.643643

Abstract

References

  • 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.
  • Hamilton, R.S., “The Ricci flow on surfaces”, Contemporary Mathematics 71 (1988) : 237-261.
  • 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.
  • Nagaraja, H.G., Venu, K., “Ricci Solitons in Kenmotsu Manifold”, Journal of Informatics and Mathematical Sciences 8 (2016) : 29.
  • Oztürk, H., “On α−Kenmotsu manifolds satisfying semi-symmetric conditions”, Konuralp Journal of Mathematics 5 (2017) : 192-193.
  • Kenmotsu, K., “A class of contact Riemannian manifold”, Tohoko Math. J. 24 (1972) : 93-103.
  • Nomizu, K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tohoko Mat. J. 20 (1968) : 46-69.
  • Blair, D.E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Mathematics 509 (1976), Springer-Verlag, Berlin.
  • Shukla, A., “Nearly trans-Sasakian manifolds”, Kuwait J. Sci. Eng. 23 (2) (1996) : 139–144.
  • Küpeli Erken, I., Piotr D., Murathan, C., “On the existence of proper nearly Kenmotsu manifolds”, Mediterr. J. Math. 13 (2016) : 4497-4507.
  • Prasad, R., Kumar, S., Gautam, U.K., “On nearly Kenmotsu manifolds with semi-symmetric metric connection”, Ganita 68 (1) (2018) : 133.
  • De, U.C., “On ϕ−recurrent Kenmotsu manifolds”, Turk J. Math. 33 (2009) : 17-25.
  • Ayar, G., Yıldırım, M., “η-Ricci solitons on nearly Kenmotsu manifolds”, Asian-European Journal of Mathematics 12 (6) (2019) : 2040002.
  • 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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Gülhan Ayar

Dilek Demirhan This is me

Publication Date December 31, 2019
Published in Issue Year 2019

Cite

APA Ayar, G., & Demirhan, D. (2019). Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. Journal of Engineering Technology and Applied Sciences, 4(3), 131-140. https://doi.org/10.30931/jetas.643643
AMA Ayar G, Demirhan D. Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. JETAS. December 2019;4(3):131-140. doi:10.30931/jetas.643643
Chicago Ayar, Gülhan, and Dilek Demirhan. “Ricci Solitons on Nearly Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Journal of Engineering Technology and Applied Sciences 4, no. 3 (December 2019): 131-40. https://doi.org/10.30931/jetas.643643.
EndNote Ayar G, Demirhan D (December 1, 2019) Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. Journal of Engineering Technology and Applied Sciences 4 3 131–140.
IEEE G. Ayar and D. Demirhan, “Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection”, JETAS, vol. 4, no. 3, pp. 131–140, 2019, doi: 10.30931/jetas.643643.
ISNAD Ayar, Gülhan - Demirhan, Dilek. “Ricci Solitons on Nearly Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Journal of Engineering Technology and Applied Sciences 4/3 (December 2019), 131-140. https://doi.org/10.30931/jetas.643643.
JAMA Ayar G, Demirhan D. Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. JETAS. 2019;4:131–140.
MLA Ayar, Gülhan and Dilek Demirhan. “Ricci Solitons on Nearly Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Journal of Engineering Technology and Applied Sciences, vol. 4, no. 3, 2019, pp. 131-40, doi:10.30931/jetas.643643.
Vancouver Ayar G, Demirhan D. Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection. JETAS. 2019;4(3):131-40.