SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Volume: 15 Issue: 2

Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton

Müslüm Aykut Akgün(ADIYAMAN ÜNİVERSİTESİ)0000-0002-8414-5228
Bilal Eftal Acet(ADIYAMAN ÜNİVERSİTESİ)0000-0002-0190-3741
Pages
—
Publication Date
2023-12-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton.
📊
Key Findings & Data:We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton.
💡
Conclusion & Impact:Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ricci soliton · conformal Ricci soliton · quasi-Sasakian manifold.

Abstract

In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.

🔖

Cite This Article

Akgün, M. A., Acet, B. E. (2023). Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. Turkish Journal of Mathematics and Computer Science, Volume: 15 Issue: 2. https://doi.org/10.47000/tjmcs.1082849

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (28)

  1. Basu, N., Bhattacharyya A., Conformal Ricci soliton in Kenmotsu manifold, Glob. J. of Adv. Research on Class. Modern Geom., 4(1)(2015), 15–21.
  2. Blaga, M.A.,η−Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2)(2016), 489–496.
  3. Blaga, M.A., Y¨uksel Perktas¸, S., Erdo˘gan, F.E., Acet, B.E., η−Ricci solitons in (ε)−almost paracontact metric manifolds, Glasnik Math., 53(1)(2018), 205–220.
  4. Blair, D.E., The theory of quasi-Sasakian structures, J. Diff Geo., 1(1967), 331–345.
  5. Calin, C., Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f−Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc., 33(3)(2010), 361–368.
  6. Cho, J.T., Kimura M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2)(2009), 205–212.
  7. De, U.C., Majhi P., φ−semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci., 21(2)(2015), 170–178.
  8. De, U.C., Mondal, A.K., 3-dimensional quasi-Sasakian manifolds and Ricci solitons, SUT J. Math., 48(1)(2012), 71–81.
  9. De, U.C., Sarkar, A., On three-dimensional quasi-Sasakian manifolds, SUT J. Math., 45(1) 2009), 59–71.
  10. De, U.C., Yildiz, A., Turan, M., Acet, B. E., 3-dimensional quasi-Sasakian manifolds with semi-symmetric non-metric connection, Hacettepe J. Math. Stat., 41(1)(2012), 127–137.
  11. De, U.C., De, K., Khan, M.N.I., Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons and Fractals, 167(2023).
  12. Fischer, A.E., An introduction to conformal Ricci flow class, Quantum Grav., 21(3)(2004), 171–218.
  13. Gautam, U.K., Haseeb, A., Prasad R., Some results on projective curvature tensor in Sasakian manifolds, Commun. Korean Math. Soc., 34(3)(2019), 881–896.
  14. Ghosh, S., η−Ricci solitons on quasi-Sasakian manifolds, An. Univ. Vest Timi¸s. Ser. Mat.-Inform., 56(1)(2018), 73–85.
  15. Gonzalez, J.C., Chinea, D., Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc., 105(1)(1989), 173–184.
  16. Haseeb, A., Prasad, R., η−Ricci solitons on ε−LP-Sasakian manifolds with a quartersymmetric metric connection, Honam Math. J., 41(3)(2019), 539–558.
  17. Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as ∗η-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
  18. Kanemaki, S., Quasi-Sasakian manifolds, Tohoku Math. J., 29(2)(1977), 227–233.
  19. Kanemaki, S., On Quasi-Sasakian manifolds in Differential Geometry, Banach Center Publ., Warsaw, 1979.
  20. Majhi, P., De, U.C., Kar, D., η−Ricci solitons on Sasakian 3-manifolds, An. Univ. Vest Timis. Ser. Mat.-Inform., 55(2)(2017), 143–156.
  21. Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math., 47(1)(1986), 41–50.
  22. Olszak, Z., On three-dimensional conformally flat quasi-Sasakian manifolds, Period. Math. Hungar., 33(2)(1996), 105–113.
  23. Pokhariyal, G.P., Mishra, R.S., Curvature tensor and their relativistic significance II, Yokohama Math. J., 19(2)(1971), 97–103.
  24. Prakasha, D.G., Hadimani, B.S., η−Ricci solitons on para-Sasakian manifolds, J. Geom., 108(2)(2017), 383–392.
  25. Sardar, A., Khan, M.N.I., De, U.C., h-*-Ricci solitons and almost co-K¨ahler manifolds, Mathematics, 9(24)(2021), 3200.
  26. Turan, M., Yetim, C., Chaubey, S.K., On quasi-Sasakian 3-manifolds admitting η−Ricci solitons, Filomat, 33(15)(2019), 4923–4930.
  27. Walker, A.G., On Ruse’s spaces of recurrent curvature, Proc. London Math. Soc., 52(2)(1950), 36–64.
  28. Yano, K., Kon, M., Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.