D-homothetically deformed Kenmotsu metric as a Ricci soliton



Abstract

In this paper we study the nature of Ricci solitons in D-homothetically deformed Kenmotsu manifolds. We prove that η-Einstein Kenmotsu metric as a Ricci soliton remains η-Einstein under D-homothetic deformation and the scalar curvature remains constant.


Keywords

Ricci solitons, Kenmotsu; D-homothetic; conformal; shrinking; expanding; steady

1. Bejan C.L., Crasmareanu M., Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46 (2014), no. 2, 117–127.
2. Blair D.E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin–Heidelberg, 1976.
3. De U.C., Yildiz A., Yalınız A.F., On ϕ-recurrent Kenmotsu manifolds, Turkish J. Math. 33 (2009), no. 1, 17–25.
4. De U.C., Ghosh S., D-homothetic deformation of normal almost contact metric manifolds, Ukrainian Math. J. 64 (2013), no. 10, 1514–1530.
5. Ghosh A., Sharma R., K-contact metrics as Ricci solitons, Beitr. Algebra Geom. 53 (2012), no. 1, 25–30.
6. Ghosh A., Sharma R., Sasakian metric as a Ricci soliton and related results, J. Geom. Phys. 75 (2014), 1–6.
7. Nagaraja H.G., Premalatha C.R., Da-homothetic deformation of K-contact manifolds, ISRN Geom. 2013, Art. ID 392608, 7 pp.
8. Nagaraja H.G., Premalatha C.R., Ricci solitons in f-Kenmotsu manifolds and 3-dimensional trans-Sasakian manifolds, Progr. Appl. Math. 3 (2012), no. 2, 1–6.
9. Nagaraja H.G., Premalatha C.R., Ricci solitons in Kenmotsu manifolds, J. Math. Anal. 3 (2012), no. 2, 18–24.
10. Shaikh A.A., Baishya K.K., Eyasmin S., On D-homothetic deformation of trans-Sasakian structure, Demonstratio Math. 41 (2008), no. 1, 171–188.
11. Sharma R., Certain results on K-contact and (k,μ)-contact manifolds, J. Geom. 89 (2008), no. 1, 138–147.
12. Sharma R., Ghosh A., Sasakian 3-manifold as a Ricci soliton represents the Heisenberg group, Int. J. Geom. Methods Mod. Phys. 8 (2011), no. 1, 149–154.
13. Tanno S., The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700–717.
14. Yano K., Integral Formulas in Riemannian Geometry, Pure and Applied Mathematics, No. 1, Marcel Dekker, Inc., New York, 1970.
15. Yildiz A., De U.C., Turan M., On 3-dimensional f-Kenmotsu manifolds and Ricci solitons, Ukrainian Math. J. 65 (2013), no. 5, 684–693.
Download

Published : 2018-12-06


Kiran KumarD., NagarajaH., & VenuK. (2018). D-homothetically deformed Kenmotsu metric as a Ricci soliton. Annales Mathematicae Silesianae, 33, 143-152. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13658

D.L. Kiran Kumar 
Department of Mathematics, Bangalore University, India  India
H.G. Nagaraja  hgnraj@yahoo.com
Department of Mathematics, Bangalore University, India  India
K. Venu 
Department of Mathematics, Faculty of Mathematical and Physical sciences, M.S. Ramaiah University of Applied Sciences, India  India



The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.