Research Article
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Year 2023, , 196 - 200, 30.04.2023
https://doi.org/10.36890/iejg.1239222

Abstract

References

  • [1] Blair, D. E.: Contact manifolds in Reimannian geometry, Lecture notes in Math. 509, Springer-verlag., 1976.
  • [2] Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons, J. Geom. Symmetry Phys., 52 (2019), 17-26.
  • [3] Chen, B. Y., Deshmukh, S.: Yamabe and quasi Yamabe solitons on Euclidean submanifolds, Mediter. J. Math., 15 (2018) article 194.
  • [4] Chen, B. Y., Deshmukh, S.: A note on Yamabe solitons, Balkan J. Geom. and its Applications, 23 (2018), 37-43.
  • [5] Calvaruso, G., Zaeim, A.: A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces, J. Geom. Phys., 80 (2014), 15-25.
  • [6] De, U. C., Mandal, K.: On a type of almost Kenmotsu manifolds with nullity distribution, Arab Journal of Mathematical Sciences, doi. org/ 10.2016/j.ajmsc.2016.04.001.
  • [7] De, U. C., Mandal, K.: On ϕ-Ricci recurrent almost Kenmotsu manifolds with nullity distribution, International Electronic Journal of Geomatry, 9(2016), 70-79.
  • [8] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46-61.
  • [9] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14(2007), 343-354.
  • [10] Deszcz. R., Hotlos, M.: On some pseudosymmetry type curvature condition, Tsukuba J. Math., 27 (2003), 13-30.
  • [11] Hamilton, R. S.: The Ricci flow on surfaces, Contemp. Math.71(1988), 237-261.
  • [12] Janssens, D., Vanhecke, L.: Almost contact structures and curvature tensors, Kodai Math J., 4(1981), 1-27.
  • [13] Kenmotsu, K.: A class of almost contact Riemannian manifolds, Tohoku Math. J. 24(1972), 93-103.
  • [14] Sharma, R.: A 3-dimensional Sasakian metric as a Yamabe solitons, Int. J. Geom. Methods Mod. Phys., 9 (2012), 1220003.
  • [15] Suh, Y. J., De, U. C.: Yamabe solitons and Ricci solitons on almost Co-Kahler manifolds, Canad. Math. Bull., 62 (2019), 653-661.
  • [16] Wang, Y.: Yamabe solitons in three dimensional Kenmotsu manifolds, Bull. Belg. Math. Soc. Simon Stevin, 23(2016), 345 − 355.
  • [17] Wang, Y., Liu, X.: Ricci solitons on three-dimensional η-Einstein almost Kenmotsu manifolds, Taiwanese J. of Math., 19(2015), 91-100.
  • [18] Wang, Y., Liu, X.: On ϕ-recurrent almost Kenmotsu manifolds, Kuwait. J. Sci., 42(2015), 65-77.
  • [19] Wang, Y.: Almost Kenmotsu (k, µ)′- manifolds with Yamabe solitons, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 115(2021), 14:8 pp.
  • [20] Wang, Y.: Almost Kenmotsu (k, µ)′- manifolds of dimension three and conformal vector fields, Int. J. Geom. Methods Mod. Phys., 19(2022), 22500054:9 pp.
  • [21] Wang, Y., Liu, X.: On the classification of almost Kenmotsu manifolds of dimension 3, Hindawi Publishing corporation, 2013, 6 pages.
  • [22] Yano, K., Kon, M.: Structures on manifolds. Vol 40, World Scientific Press, 1989.

A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$

Year 2023, , 196 - 200, 30.04.2023
https://doi.org/10.36890/iejg.1239222

Abstract

In the present paper, we prove that if the metric of a three dimensional almost Kenmotsu manifold with $\textbf{Q}\phi=\phi \textbf{Q}$ whose scalar curvature remains invariant under the chracterstic vector field $\zeta$, admits a non-trivial Yamabe solitons, then the manifold is of constant sectional curvature or the manifold is Ricci simple.

References

  • [1] Blair, D. E.: Contact manifolds in Reimannian geometry, Lecture notes in Math. 509, Springer-verlag., 1976.
  • [2] Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons, J. Geom. Symmetry Phys., 52 (2019), 17-26.
  • [3] Chen, B. Y., Deshmukh, S.: Yamabe and quasi Yamabe solitons on Euclidean submanifolds, Mediter. J. Math., 15 (2018) article 194.
  • [4] Chen, B. Y., Deshmukh, S.: A note on Yamabe solitons, Balkan J. Geom. and its Applications, 23 (2018), 37-43.
  • [5] Calvaruso, G., Zaeim, A.: A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces, J. Geom. Phys., 80 (2014), 15-25.
  • [6] De, U. C., Mandal, K.: On a type of almost Kenmotsu manifolds with nullity distribution, Arab Journal of Mathematical Sciences, doi. org/ 10.2016/j.ajmsc.2016.04.001.
  • [7] De, U. C., Mandal, K.: On ϕ-Ricci recurrent almost Kenmotsu manifolds with nullity distribution, International Electronic Journal of Geomatry, 9(2016), 70-79.
  • [8] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46-61.
  • [9] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14(2007), 343-354.
  • [10] Deszcz. R., Hotlos, M.: On some pseudosymmetry type curvature condition, Tsukuba J. Math., 27 (2003), 13-30.
  • [11] Hamilton, R. S.: The Ricci flow on surfaces, Contemp. Math.71(1988), 237-261.
  • [12] Janssens, D., Vanhecke, L.: Almost contact structures and curvature tensors, Kodai Math J., 4(1981), 1-27.
  • [13] Kenmotsu, K.: A class of almost contact Riemannian manifolds, Tohoku Math. J. 24(1972), 93-103.
  • [14] Sharma, R.: A 3-dimensional Sasakian metric as a Yamabe solitons, Int. J. Geom. Methods Mod. Phys., 9 (2012), 1220003.
  • [15] Suh, Y. J., De, U. C.: Yamabe solitons and Ricci solitons on almost Co-Kahler manifolds, Canad. Math. Bull., 62 (2019), 653-661.
  • [16] Wang, Y.: Yamabe solitons in three dimensional Kenmotsu manifolds, Bull. Belg. Math. Soc. Simon Stevin, 23(2016), 345 − 355.
  • [17] Wang, Y., Liu, X.: Ricci solitons on three-dimensional η-Einstein almost Kenmotsu manifolds, Taiwanese J. of Math., 19(2015), 91-100.
  • [18] Wang, Y., Liu, X.: On ϕ-recurrent almost Kenmotsu manifolds, Kuwait. J. Sci., 42(2015), 65-77.
  • [19] Wang, Y.: Almost Kenmotsu (k, µ)′- manifolds with Yamabe solitons, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 115(2021), 14:8 pp.
  • [20] Wang, Y.: Almost Kenmotsu (k, µ)′- manifolds of dimension three and conformal vector fields, Int. J. Geom. Methods Mod. Phys., 19(2022), 22500054:9 pp.
  • [21] Wang, Y., Liu, X.: On the classification of almost Kenmotsu manifolds of dimension 3, Hindawi Publishing corporation, 2013, 6 pages.
  • [22] Yano, K., Kon, M.: Structures on manifolds. Vol 40, World Scientific Press, 1989.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Gopal Ghosh 0000-0001-6178-6340

Publication Date April 30, 2023
Acceptance Date March 4, 2023
Published in Issue Year 2023

Cite

APA Ghosh, G. (2023). A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$. International Electronic Journal of Geometry, 16(1), 196-200. https://doi.org/10.36890/iejg.1239222
AMA Ghosh G. A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$. Int. Electron. J. Geom. April 2023;16(1):196-200. doi:10.36890/iejg.1239222
Chicago Ghosh, Gopal. “A Note on Yamabe Solitons on 3-Dimensional Almost Kenmotsu Manifolds With $\: \textbf{Q}\phi=\phi \textbf{Q}$”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 196-200. https://doi.org/10.36890/iejg.1239222.
EndNote Ghosh G (April 1, 2023) A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$. International Electronic Journal of Geometry 16 1 196–200.
IEEE G. Ghosh, “A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 196–200, 2023, doi: 10.36890/iejg.1239222.
ISNAD Ghosh, Gopal. “A Note on Yamabe Solitons on 3-Dimensional Almost Kenmotsu Manifolds With $\: \textbf{Q}\phi=\phi \textbf{Q}$”. International Electronic Journal of Geometry 16/1 (April 2023), 196-200. https://doi.org/10.36890/iejg.1239222.
JAMA Ghosh G. A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$. Int. Electron. J. Geom. 2023;16:196–200.
MLA Ghosh, Gopal. “A Note on Yamabe Solitons on 3-Dimensional Almost Kenmotsu Manifolds With $\: \textbf{Q}\phi=\phi \textbf{Q}$”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 196-00, doi:10.36890/iejg.1239222.
Vancouver Ghosh G. A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$. Int. Electron. J. Geom. 2023;16(1):196-200.