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Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 5، شماره 4، 2024، صفحه 305-319 اصل مقاله (410.6 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22329.1153 | ||
| نویسندگان | ||
| Ghodratallah Fasihi Ramandi* 1؛ Shahroud Azami2؛ Vahid Pirhadi3 | ||
| 1Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran | ||
| 2Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran | ||
| 3Department of Pure Mathematics, Faculty of mathematics, University of Kashan, Kashan, Iran | ||
| چکیده | ||
| In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat = \lambda g$ associated to the Bott connection $\nabla^B$, here ${X}$ is a vector field and $\lambda , a, b, c$ are real constants such that $c\neq 0$. A complete classification of this structure on $3$-dimensional Lorentzian Lie groups will be presented. | ||
| کلیدواژهها | ||
| Left-invariant Lorentz metric؛ Generalized Ricci soliton؛ Pseudo-Riemannian metric؛ Lie group | ||
| مراجع | ||
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[1] J. A. Alvarez Lopez and P. Tondeur ´ , Hodge decomposition along the leaves of a Riemannian foliation, J. Funct. Anal., 99 (1991), pp. 443–458.
[2] S. Azami, Affine generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated to Yano connection, J. Nonlinear Math. Phys., 30 (2023), pp. 719–742.
[3] , Generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-Nomizu connections, J. Nonlinear Math. Phys., 30 (2023), pp. 1–33.
[4] W. Batat and K. Onda, Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, J. Geom. Phys., 114 (2017), pp. 138–152.
[5] F. Baudoin, Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations, in Geometry, analysis and dynamics on sub-Riemannian manifolds. Vol. 1, EMS Ser. Lect. Math., Eur. Math. Soc., Z¨urich, 2016, pp. 259–321.
[6] B. Bidabad and M. K. Sedaghat, Ricci flow on Finsler surfaces, J. Geom. Phys., 129 (2018), pp. 238–254.
[7] N. Bokan, T. Sukilovi ˇ c, and S. Vukmirovi ´ c´, Lorentz geometry of 4-dimensional nilpotent Lie groups, Geom. Dedicata, 177 (2015), pp. 83–102.
[8] G. Catino, P. Mastrolia, D. D. Monticelli, and M. Rigoli, On the geometry of gradient Einstein-type manifolds, Pacific J. Math., 286 (2017), pp. 39–67.
[9] B. Chow, P. Lu, and L. Ni, Hamilton’s Ricci flow, vol. 77 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI; Science Press Beijing, New York, 2006.
[10] M. Crasmareanu, A new approach to gradient Ricci solitons and generalizations, Filomat, 32 (2018), pp. 3337–3346.
[11] N. G. Halammanavar and K. K. L. Devasandra, Kenmotsu manifolds admitting Schouten–van Kampen connection, Facta Univ. Ser. Math. Inform., 34 (2019), pp. 23–34.
[12] Y. Han, A. De, and P. Zhao, On a semi-quasi-Einstein manifold, J. Geom. Phys., 155 (2020), pp. 103739, 8.
[13] S. K. Hui, R. Prasad, and D. Chakraborty, Ricci solitons on Kenmotsu manifolds with respect to quarter symmetric non-metric ϕ-connection, Ganita, 67 (2017), pp. 195–204.
[14] K. Onda, Lorentz Ricci solitons on 3-dimensional Lie groups, Geom. Dedicata, 147 (2010), pp. 313–322.
[15] C. Ozg ¨ ur and S. Sular ¨ , Warped products with a semi-symmetric non-metric connection, Arab. J. Sci. Eng., 36 (2011), pp. 461–473.
[16] G. Perelman, The entropy formula for the ricci flow and its geometric applications, 2002.
[17] S. Y. Perktas¸ and A. Yı ldız, On quasi-Sasakian 3-manifolds with respect to the Schouten–van Kampen connection, Int. Electron. J. Geom., 13 (2020), pp. 62–74.
[18] Q. Qu and Y. Wang, Multiply warped products with a quarter-symmetric connection, J. Math. Anal. Appl., 431 (2015), pp. 955–987.
[19] A. N. Siddiqui, B.-Y. Chen, and O. Bahadir, Statistical solitons and inequalities for statistical warped product submanifolds, Mathematics, 7 (2019), pp. 1701–1719.
[20] S. Sular and C. Ozg ¨ ur¨ , Warped products with a semi-symmetric metric connection, Taiwanese J. Math., 15 (2011), pp. 1701–1719.
[21] Y. Wang, Curvature of multiply warped products with an affine connection, Bull. Korean Math. Soc., 50 (2013), pp. 1567–1586.
[22] , Multiply warped products with a semisymmetric metric connection, Abstr. Appl. Anal., (2014), pp. Art. ID 742371, 12.
[23] , Affine Ricci solitons of three-dimensional Lorentzian Lie groups, J. Nonlinear Math. Phys., 28 (2021), pp. 277–291.
[24] , Canonical connections and algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, Chinese Ann. Math. Ser. B, 43 (2022), pp. 443–458.
[25] T. H. Wears, On Lorentzian Ricci solitons on nilpotent Lie groups, Math. Nachr., 290 (2017), pp. 1381–1405.
[26] M. Yar Ahmadi and B. Bidabad, On compact Ricci solitons in Finsler geometry, C. R. Math. Acad. Sci. Paris, 353 (2015), pp. 1023–1027. | ||
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