مجله مدل‌سازی پیشرفته ریاضی

مجله مدل‌سازی پیشرفته ریاضی

HOMOGENEOUS GENERALIZED RICCI SOLITONS ON THE LANCZOS UNIVERSE

نوع مقاله : مقاله پژوهشی

نویسندگان
1 Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran.
2 Department of Physics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran.
چکیده
This work is devoted to the study of Killing vector fields associated with Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. After establishing the general properties of these symmetries, we narrow our attention to a distinguished subclass of FLRW models, known as the Lanczos universe. For this particular family of homogeneous spacetimes, we develop an algebraic description that captures their essential geometric structure. Utilizing this algebraic perspective, we further explore the
کلیدواژه‌ها
موضوعات

1] Calderbank, D.M.J. and Pedersen, H., 1999. Einstein-Weyl Geometry In: Surveys in differential
geometry: Essays on Einstein manifolds. Surveys in Differential Geometry, 6, pp. 387–423.
[2] Calvaruso, G., 2018. The Ricci soliton equation and the structure of homogeneous G¨odel-type spacetimes. J. Math. Anal. Appl., 465(2), 1112–1133. doi:10.1016/j.jmaa.2018.05.051
[3] Calvaruso, G., 2017. Three-Dimensional Homogeneous Generalized Ricci Solitons. Mediterranean
Journal of Mathematics, 14(5)(2017), Article 216. doi:10.1007/s00009-017-1019-2
[4] Calvi˜no-Louzao, E., Garcia-Rio, E. and Vazquez-Lorenzo R., 2017. Ricci Solitons: Aspects of differential geometry III. Springer Cham. doi:10.1007/978-3-031-02410-8.
[5] Cao, H.-D., 2010. Recent progress on Ricci solitons. Recent Advances in Geometric Analysis, Adv.
Lect. Math. (ALM) 11, Int. Press, Somerville, MA, pp. 1–38. doi:10.48550/arXiv.0908.2006
[6] Dodelson, S. and Fabian, S., 2020. Modern Cosmology. London: Academic Press. doi:10.1016/C2017-
0-01943-2
[7] Ellis, G.F.R., Maartens, R. and MacCallum, M.A.H., 2012. Relativistic Cosmology. Cambridge University Press. www.cambridge.org/9780521381154
[8] Fels, M. E. and Renner, A. G., 2006. Non-reductive homogeneous pseudo-Riemannian manifolds of
dimension four. Canadian Journal of Mathematics, 58(2), pp. 282–311. doi:10.4153/CJM-2006-012-1
[9] Griffiths, J. B. and Podolsk´y, J., 2009. Exact Space-Times in Einstein’s General Relativity. Cambridge University Press. doi:10.1017/CBO9780511635397
[10] Hamilton, R. S., 1988. The Ricci flow on surfaces. Contemporary Mathematics, 71, 237–261.
doi:10.1090/conm/071/954419
[11] Hawking, S.W. and Ellis, G.F.R., 1973. The Large Scale Structure of Space-Time. Cambridge University Press. doi:10.1017/CBO9780511524646
[12] Kumara H. A., Naik D. M. and Venkatesha V., 2022. Geometry of generalized Ricci-type solitons on
a class of Riemannian manifolds. J. Geom. Phys. 175, 104507. doi:10.1016/j.geomphys.2022.104506
[13] Lanczos, C., 1924. Uber eine station¨are Kosmologie im Sinne der Einsteinischen Gravitationstheorie. ¨
Zeitschrift f¨ur Physik, 21, pp. 73–110.
[14] Mukhanov, V., 2005. Physical Foundations of Cosmology. Cambridge University Press.
doi:10.1017/CBO9780511790553
[15] Nurowski, P. and Randall, M., 2016. Generalised Ricci Solitons. J. Geometric Analysis, 26, pp.
1280–1345. doi:10.1007/s12220-015-9592-8
[16] O’Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press.
doi:10.1112/blms/16.3.328
[17] Peebles, P. J. E., 1993. Principles of Physical Cosmology. Princeton University Press.
doi:10.1515/9780691206721
[18] Pirhadi, V., Fasihi-Ramandi, G. and Azami, S., 2023. Generalized Ricci Solitons on ThreeDimensional Lorentzian Walker Manifolds. J. Nonlinear Mathematical Physics, 30, pp. 1409–1423.
doi:10.1007/s44198-023-00134-4
[19] Randall, M., 2014. Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor.
J. Geom. Phys., 76, pp. 192–199. doi:10.1016/j.geomphys.2013.10.019
[20] Ryden, B., 2017. Introduction to Cosmology, Cambridge University Press.
doi:10.1017/9781316651087
[21] Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C. and Herlt, E., 2003. Exact Solutions of
Einstein’s Field Equations. Cambridge University Press. doi:10.1017/CBO9780511535185
22] Weinberg, S., 1972. Gravitation and Cosmology: Principles and Applications of the General Theory
of Relativity, John Wiley and Sons, New York.
[23] Zaeim, A., Cheshmavar J. and Musavi, M., 2024. Generalized Ricci Solitons on Homogeneous Siklos Space-times. AUT Journal of Mathematics and Computing, 5(2), pp. 131–142.
doi:10.22060/AJMC.2023.22164.1138
دوره 15، شماره 2 - شماره پیاپی 38
تابستان 1404
صفحه 113-133

  • تاریخ دریافت 08 تیر 1404
  • تاریخ بازنگری 22 مهر 1404
  • تاریخ پذیرش 26 آذر 1404