Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds

Year 2023, , 451 - 463, 29.10.2023

İrem Küpeli Erken , Mustafa Özkan , Büşra Savur

https://doi.org/10.36890/iejg.1316716

Cited By: 1

Abstract

In this paper, we study Cotton solitons on three-dimensional almost α-paracosymplectic manifolds. We especially focus on threedimensional almost α-paracosymplectic manifolds with harmonic vector field ξ and characterize them for all possible types of operator h. Finally, we constructed an example which satisfies our results.

Keywords

Cotton soliton, almost para-Kenmotsu manifold, almost paracosymplectic manifold

References

• [1] Aliev, A. N., Nutku, Y.: A theorem on topologically massive gravity. Class. Quantum Grav. 13, L29–L32 (1996).
• [2] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. in: Progress Math. vol.203, Birkhäuser, Boston, MA, (2010).
• [3] Calviño-Louzao, E., Garcia-Rio, E., Vázquez-Lorenzo, R.: A note on compact Cotton solitons. Classical Quantum Gravity. 29, 205014 (5pp)(2012).
• [4] Calviño-Louzao, E., Hervella, L.M., Seoane-Bascoy, J., Vázquez-Lorenzo, R.: Homogeneous Cotton solitons. J. Phys. A: Math. Theor. 46, 285204 (19pp) (2013).
• [5] Cappelletti-Montano, B., Nicola, A. D., Yudin, I.: A survey on cosymplectic geometry. Rev. Math. Phys. 25 (10), (2013).
• [6] Chen, X.: Cotton Solitons on Almost coKähler 3-Manifolds. Quaest. Math. 44 (8), 1055-1075 (2021).
• [7] Chen, X.: Three dimensional contact metric manifolds with Cotton solitons. Hiroshima Math. J. 51, 275-299 (2021).
• [8] Chow, D. D. K., Pope, C. N., Sezgin, E.: Classification of solutions in topologically massive gravity. Class. Quantum Grav. 27, 105001 (2010).
• [9] Dacko, P.: On almost para-cosymplectic manifolds. Tsukuba J. Math. 28, 193-213 (2004).
• [10] Dacko, P.: Five dimensional almost para-cosymplectic manifolds with contact Ricci potential. Preprint arxiv:1308.6429 (2013).
• [11] De, K., De, U.C.: Riemann solitons on para-Sasakian geometry. Carpathian Mathematical Publications. 14 (2), 395-405 (2022).
• [12] De, U.C., Khan, M.N. İ., Sardar, A.: h-Almost Ricci–Yamabe Solitons in Paracontact Geometry. Mathematics. 10, 3388, (2022).
• [13] Ferreiro Pérez, R.: Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms. Class. Quantum Grav. 27, 135015(2010).
• [14] Garcia, A. A., Hehl, F. W., Heinicke, C., Macias, A.: The Cotton tensor in Riemannian spacetimes. Class. Quantum Grav. 21 (4), 1099 (2004).
• [15] Guven, J.: Chern–Simons theory and three-dimensional surfaces. Class. Quantum Grav. 24, 1833 (2007).
• [16] Hamilton, R.S.: The Ricci-flow on surfaces. Mathematics and General Relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, (1988).
• [17] Hamilton, R.S.: Lectures on Geometric Flows. Unpublished manuscript. (1989).
• [18] Kaneyuki, S., Williams, F. L.: Almost paracontact and parahodge structure manifolds. Nagoya Math. J. 99, 173-187 (1985).
• [19] Kişisel, A. U. Ö., Sarıoğlu, Ö., Tekin, B.: Cotton flow. Class. Quantum Grav., 25 (16), 165019 (2008).
• [20] Küpeli Erken, İ, Dacko, P., Murathan, C.: Almost α-paracosymplectic manifolds. J. Geom. Phys. 88, 30-51 (2015).
• [21] Küpeli Erken, İ., Murathan, C.: A study of three-dimensional paracontact (˜κ, ˜μ, ˜v)− spaces. Int. J. Geom. Methods Mod. Phys. 14 (7), 35pp (2017).
• [22] Küpeli Erken, İ: Yamabe solitons on three-dimensional normal almost paracontact metric manifolds. Periodica Mathematica Hungarica 80 (2), 172-184 (2020).
• [23] Lashkari, N., Maloney, A.: Topologically massive gravity and Ricci–Cotton flow. Class. Quantum Grav. 28, 105007 (2011).
• [24] Martin-Molina, V.: Paracontact metric manifolds without a contact metric counterpart. Taiwanese Journal of Mathematics. 19 (1), 175–191 (2015).
• [25] Ozkan, M., Küpeli Erken, I., Murathan, C.: Cotton solitons on three dimensional paracontact metric manifolds. Filomat. 37 (15), 5109-5121 (2023).
• [26] Welyczko, J.: On basic curvature identities for almost (para)contact metric manifolds. Preprint arxiv:1209.4731 (2012).
• [27] Weyl, H.: Reine Infinitesimal geometric. Math. Zeitschr. 2, 384-411 (1918).
• [28] Zamkovoy, S.: Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36, 37-60 (2009).