Korean Journal of Mathematics

  • 제29권2호
  • /
  • Pages.445-453
  • /
  • 2021
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

PARA-KENMOTSU METRIC AS A 𝜂-RICCI SOLITON

  • 투고 : 2021.01.21
  • 심사 : 2021.05.21
  • 발행 : 2021.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of the paper is to study of Para-Kenmotsu metric as a 𝜂-Ricci soliton. The paper is organized as follows: • If an 𝜂-Einstein para-Kenmotsu metric represents an 𝜂-Ricci soliton with flow vector field V, then it is Einstein with constant scalar curvature r = -2n(2n + 1). • If a para-Kenmotsu metric g represents an 𝜂-Ricci soliton with the flow vector field V being an infinitesimal paracontact transformation, then V is strict and the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). • If a para-Kenmotsu metric g represents an 𝜂-Ricci soliton with non-zero flow vector field V being collinear with 𝜉, then the manifold is an Einstein manifold with constant scalar curvature r = -2n(2n + 1). Finally, we cited few examples to illustrate the results obtained.

키워드

과제정보

The author gratefully thank to the Referee for the constructive comments and recommendations which definitely help to improve the readability and quality of the paper.

참고문헌

  1. Bejan, C.L., Crasmareanu, M., Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Annals of Global Analysis and Geometry volume 46 (2014), 117-127. https://doi.org/10.1007/s10455-014-9414-4
  2. Calvaruso, G., Perrone, D., Geometry of H-paracontact metric manifolds, arxiv:1307.7662v1. 2013.
  3. Calin, C.,Crasmareanu, M., η-Ricci solitons on Hopf hypersurfaces in complex space forms, Revue Roumaine de Mathematiques pures et appliques 57 (1) (2012), 55-63.
  4. Chow, B. and Knopf, D., The Ricci Flow, An Introduction, AMS 2004.
  5. Chodosh, O. and Fong,F.T.H., Rotational symmetry of conical Kahler-Ricci solitons, arxiv:1304.0277v2. 2013. https://doi.org/10.1007/s00208-015-1240-x
  6. Cho, J.T., Kimura,M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J 61 (2) (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
  7. Calin, C.,Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malaysian Math. Sci. Soc. 33 (3) (2010), 361-368.
  8. Futaki, A., Ono, H., Wang, H., Transverse Kahler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds, J. Diff. Geom 83 (3) (2009), 585-636.
  9. Ghosh, A., An η-Einstein Kenmotsu metric as a Ricci soliton, Publ. Math. Debrecen 2013.
  10. Ghosh, A., Ricci Solitons and Contact Metric Manifolds, Glasgow Mathematical Journal 55 (1) (2013), 123-130. https://doi.org/10.1017/s0017089512000389
  11. Hamilton, R. S., Lectures on geometric flows, unpublished manuscript 1989.
  12. Kundu, S., α-Sasakian 3-Metric as a Ricci Soliton, Ukrainian Mathematical Journal 65(6), November, 2013.
  13. Patra, D.S., Rovenski, V., Almost η-Ricci solitons on Kenmotsu manifolds, European Journal of Mathematics 2021.
  14. Patra, D.S., Ricci Solitons and Paracontact Geometry, Mediterranean Journal of Mathematics 16 Article number: 137 (2019).
  15. Patra, D.S., Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold, Bull. Korean Math. Soc. 56 (5) (2019), 1315-1325. https://doi.org/10.4134/bkms.b181175
  16. Schouten, J. A., Ricci Calculus, Springer-Verlag, Berlin, 2nd Ed.(1954), pp. 332.
  17. Sharma, R., Certain results on K-contact and (κ, µ)-contact manifolds, J. Geom 89 (1-2) (2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5
  18. Yano, K., Integral Formulas in Riemannian Geometry, Marcel Dekker, New York 1970.
  19. Zamkovoy, S., On Para-Kenmotsu Manifolds, Filomat 32:14 (2018), 4971-4980. https://doi.org/10.2298/fil1814971z