Abstract
We classify, up to isometry, non-symmetric simply-connected four-dimensional pseudo-Riemannian generalized symmetric spaces which are algebraic Ricci solitons. It turns out that those of Cerny–Kowalski’s types A, C and D are algebraic Ricci solitons, whereas those of type B are not. Thus, we give new examples of algebraic Ricci solitons.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Batat, W., Onda, K.: Algebraic Ricci solitons on three-dimensional Lorentzian lie groups (arXiv:1112.2455)
Calvaruso G.: Homogeneous structures on three-dimensional Lorentzian manifolds. J. Geom. Phys. 57(4), 1279–1291 (2007)
Calvaruso G., de Leo B.: Curvature properties of four-dimensional generalized symmetric spaces. J. Geom. 90, 30–46 (2008)
Cerny J., Kowalski O.: Classification of generalized symmetric pseudo-Riemannian spaces of dimension n = 4. Tensor N.S. 38, 256–267 (1982)
de Leo B., Marinosci R.A.: Homogeneous geodesics of four-dimensional generalized symmetric pseudo-Riemannian spaces. Publ.Math. Debrecen. 73, 341–360 (2008)
de Leo B., der Veken J.V.: Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces. Geometriae Dedicata 159(1), 373–387 (2012)
Fels M.E., Renner A.G.: Non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Can. J. Math. 58(2), 282–311 (2006)
Jablonski, M.: Homogeneous Ricci solitons (arXiv:1109.6556)
Lauret J.: Ricci soliton homogeneous nilmanifolds. Math. Ann. 319(4), 715–733 (2001)
Onda, K.: Examples of algebraic Ricci solitons in the pseudo-Riemannian case (arXiv: 1112.0424)
O’Neill B.: Semi-Riemannian geometry. Academic Press, New York (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
W. Batat was supported by funds of JSPS; ENPO; and Ministry of Economy and Competitiveness, Spain, under project MTM2011-22528. K. Onda was partially supported by the JSPS Institutional Program for Young Researcher Overseas Visits Promoting international young researchers in mathematics and mathematical sciences led by OCAMIh.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Batat, W., Onda, K. Four-Dimensional Pseudo-Riemannian Generalized Symmetric Spaces Which are Algebraic Ricci Solitons. Results. Math. 64, 253–267 (2013). https://doi.org/10.1007/s00025-013-0312-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-013-0312-z