RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE MODEL SPACE $Sol^{4}_{0}$

Mahin Sohrabpour, Shahroud Azami

DOI Number
https://doi.org/10.22190/FUMI240731045S
First page
655
Last page
669

Abstract


In this paper, we classify the Ricci solitons and the Ricci bi-conformal vector fields on model space $Sol^{4}_{0}$. We also show which of them are gradient vector fields and which one of those are Killing vector fields.

Keywords

Ricci solitons, vector fields, manifolds

Full Text:

PDF

References


P. Atashpeykar and A. Haji-Badali: The algebraic Ricci solitons of Lie group H2 ×R and Sol3. Journal of Finsler Geometry and its Applications, 1(2) (2020), 105–114.

S. Azami and U. C. De: Ricci bi-conformal vector fields on Lorentzian fivedimensional two-step nilpotent Lie groups. Hacet. J. Math. Stat. (2023), 10.15672/hujms. 1294973.

S. Azami and G. Fasihi-Ramandi: Ricci bi-conformal vector fields on Siklos spacetimes. Mathematics. Interdisciplinary research, 9(1) (2024), 45–76.

S. Azami and M. Jafari: Ricci bi-conformal vector fields on homogeneous Gödel-type spacetimes. J. nonlinear Math. Phys. 30 (2023), 1700–1718.

S. Azami and M. Jafari: Ricci solitons and Ricci bi-conformal vector fields on H2×R. Report on mathematical physics, 93(2) (2024), 231–239.

M. Brozos-Vazquez, G. Calvaruso, E. Garcia-Rio and S. Gavino-Fernandez: Three-dimensional Lorentzian homogeneous Ricci solitons. Israel J. Math., 188 (2012), 385–403.

U. C. De, A. Sardar and A. Sarkar: Some conformal vector fields and conformal Ricci solitons on N(k)-contact metric manifolds. AUT J. Math. Com., 2(1) (2021), 61–71.

S. Deshmukh: Geometry of Conformal Vector Fields. Arab. J. Math., 23(1) (2017), 44–73.

S. Deshmukh and F. R. Al-Solamy: Conformal Vector Fields on a Riemannian Manifold. Balkan Journal of Geometry and its Application, 19(2) (2014), 86–93.

Z. Erjavec: Geodesics and Translation Curves in Sol40. Mathematics, 11 (2023), 1533.

Z. Erjavec and J. Inoguchi: Minimal submanifolds in Sol4

J. Geom. Anal. 117(156) (2023).

Z. Erjavecand J. Inoguchi: J-trajectories in 4-dimensional solvable Lie groups Sol40. Journal of Nonlinear Science, 33(111) (2023).

R. Filipkiewicz: Four dimensional geometries. Ph.D. Thesis, University of Warwick, (1983).

W. Graf: Ricci flow gravity. PMC Phys. 3 (2007).

A. Garcia-Parrado and J. M. M. Senivilla: Bi-conformal vector fields and their applications. Classical and Quantum Gravity, 21(8) (2004), 2153–2177.

R. S. Hamilton: The Ricci flow on surfaces. Contemp. Math, 71 (1988), 237–261.

V. G. Ivancevic and T. T. Ivancevic: Ricci flow and nonlinear reaction-diffusion systems in biology. chemistry, and physics. Nonlinear PS, 1 (2011), 35–54.

M. D’haene, J. I. Inguchi and J. V. D. Veken: Parallel and totally umbilical hypersurfaces of the four-dimensional Thurston geometry Sol40. Mathematische Nachrichten, 1 (2023).

M. Sohrabpour and S. Azami: Ricci bi-conformal vector fields on Lorentzian Walker manifolds of low dimension. Lobachevskii Journal of mathematics, 44(12) (2023), 5437-5443.

E. Moln´ar and B. K. Szilagyi: Translation curves and their spheres in homogeneous geometries. Publ. Math. Debrecen, 78(2) (2011), 327–346.

R. S. Sandhu, T. T. Georjiou and A. R. Tannenbaum: Ricci curvature: An economic indicator for market fragility and system risk. Sci. Adv. 2(5) (2016).

P. Scott: The geometries of 3-manifolds. Bull. London Math, 15 (1983), 15, 401–487.

W. P. Thurston: Three-dimensional geometry and topology I. Princeton Math. Series, (S. Levy ed.), Princeton University Press, 1 (1997), 1–328.

C. T. C. Wall: Geometric structures on compact complex analytic surfaces. Topology, 25(2) (1986), 119–153.

Y. Wang, X. Gu, T. F. Chan, P. M. Thompson and S. T. Yau: Brain surface conformal parametrization with the Ricci flow. IEEE Trans. Med. Imaging, 31(2), (2012), 251–264.

K. Yano: Integral formulas in Riemannian geometry. M. Dekker, (1970), ISBN 0824718070, 9780824718077.




DOI: https://doi.org/10.22190/FUMI240731045S

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)