From Ricci Soliton to Almost Contact Metric Structures

Year 2024, , 496 - 506, 27.10.2024

Beldjilali Gherici

https://doi.org/10.36890/iejg.1472479

Abstract

In this paper, we construct almost contact metric structures on a three-dimensional Riemannian manifold equipped with an almost Ricci soliton. Then, we give the techniques necessary to define the nature of such structures. Concrete examples are given.

Keywords

Almost contact metric structure, trans-Sasakian manifolds, $C_{12}$-manifolds, Ricci soliton.

Supporting Institution

No

References

• [1] Bayour, B., Beldjilali, G.: Ricci solitons on 3-dimensional C12-Manifolds. Balkan J. Geo. and Its. Appl., 27 No.2, 26-36 (2022).
• [2] Bayour, B., Beldjilali, G., Sinacer, M. A.: Almost contact metric manifolds with certain condition. Annals of Global Analysis and Geometry. 64, 12 (2023), doi.org/10.1007/s10455-023-09917-w.
• [3] Beldjilali, G.: 3-dimensional C12-Manifolds. Revista Uni. Mat. Argentina, 67 No.1, 1-14 (2024). doi.org/10.33044/revuma.3088.
• [4] Beldjilali, G.: Slant curves on 3-dimensional C12-Manifolds. Balkan J. of Geo. and Its App., 27 No.2, 13-25 (2022).
• [5] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics Vol. 203, (2002) Birhauser, Boston.
• [6] Bouzir, H., Beldjilali, G., Bayour, B.: On Three Dimensional C12-Manifolds. Mediterr. J. Math., 18, 239 (2021). doi.org/10.1007/s00009-021- 01921-3.
• [7] De, U. C., Tripathi, M. M.: Tensor in 3-dimensional Trans-Sasakian Manifolds. Kyungpook Math. J., 43, 247-255 (2003).
• [8] Ghosh, A.: Sharma, R.: Sasakian metric as a Ricci soliton and related results. J. Geom. Phys., 75, 1-6 (2014).
• [9] Ghosh, A.: Kenmotsu 3-metric as a Ricci soliton Chaos, Solitons and Fractals, 44, 647-650 (2011).
• [10] Hamilton, R. S.: The Ricci flow on surfaces, Mathematics and general relativity. 71, 237-262 (1998).
• [11] Nagaraja, H. G.: Premalatha, C. R.: Ricci solitons in Kenmotsu manifold. Journal of Mathematical Analysis, 3(2),18-24 (2012).
• [12] Olszak, Z.: Normal almost contact manifolds of dimension three. Annales Pol. Math. XLVII, 41-50 (1986).
• [13] Oubina, J. A.: New classes of almost contact metric structures. Publ. Math. Debrecen, 32, 187-193 (1985).
• [14] Pigola, S., Rigoli, M., Rimoldi, M., Setti, A. G.: Ricci Almost Solitons Ann. Scuola. Norm. Sup. Pisa Cl. Sci. 5 Vol. X , 757-79 (2011).
• [15] Sharma, R.: Certain results on K-contact and (κ, μ)-contact manifolds. J. Geom., 89 no.1, 138-147 (2008).
• [16] Tripathi, M. M.: Ricci solitons in contact metric manifolds, arXiv:0801, 4222v1, [mathDG], (2008).
• [17] Yano, K., Kon, M.: Structures on Manifolds, Series in Pure Math., World Sci, Vol 3 (1984).