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

Year 2023, Volume: 16 Issue: 2, 451 - 463, 29.10.2023
https://doi.org/10.36890/iejg.1316716

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.

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).
Year 2023, Volume: 16 Issue: 2, 451 - 463, 29.10.2023
https://doi.org/10.36890/iejg.1316716

Abstract

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).
There are 28 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

İrem Küpeli Erken 0000-0003-4471-3291

Mustafa Özkan 0000-0002-4483-2912

Büşra Savur 0000-0002-1403-5218

Early Pub Date October 6, 2023
Publication Date October 29, 2023
Acceptance Date September 7, 2023
Published in Issue Year 2023 Volume: 16 Issue: 2

Cite

APA Küpeli Erken, İ., Özkan, M., & Savur, B. (2023). Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds. International Electronic Journal of Geometry, 16(2), 451-463. https://doi.org/10.36890/iejg.1316716
AMA Küpeli Erken İ, Özkan M, Savur B. Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds. Int. Electron. J. Geom. October 2023;16(2):451-463. doi:10.36890/iejg.1316716
Chicago Küpeli Erken, İrem, Mustafa Özkan, and Büşra Savur. “Cotton Solitons on Three Dimensional Almost $\alpha$-Paracosymplectic Manifolds”. International Electronic Journal of Geometry 16, no. 2 (October 2023): 451-63. https://doi.org/10.36890/iejg.1316716.
EndNote Küpeli Erken İ, Özkan M, Savur B (October 1, 2023) Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds. International Electronic Journal of Geometry 16 2 451–463.
IEEE İ. Küpeli Erken, M. Özkan, and B. Savur, “Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds”, Int. Electron. J. Geom., vol. 16, no. 2, pp. 451–463, 2023, doi: 10.36890/iejg.1316716.
ISNAD Küpeli Erken, İrem et al. “Cotton Solitons on Three Dimensional Almost $\alpha$-Paracosymplectic Manifolds”. International Electronic Journal of Geometry 16/2 (October 2023), 451-463. https://doi.org/10.36890/iejg.1316716.
JAMA Küpeli Erken İ, Özkan M, Savur B. Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds. Int. Electron. J. Geom. 2023;16:451–463.
MLA Küpeli Erken, İrem et al. “Cotton Solitons on Three Dimensional Almost $\alpha$-Paracosymplectic Manifolds”. International Electronic Journal of Geometry, vol. 16, no. 2, 2023, pp. 451-63, doi:10.36890/iejg.1316716.
Vancouver Küpeli Erken İ, Özkan M, Savur B. Cotton Solitons on Three Dimensional Almost $\alpha$-paracosymplectic Manifolds. Int. Electron. J. Geom. 2023;16(2):451-63.