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Tytuł artykułu

A complete classification of four-dimensional paraKähler Lie algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-24
zaakceptowano
2015-01-10
online
2015-02-09
Twórcy
  • Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento,
    Prov. Lecce-Arnesano, 73100 Lecce, Italy
Bibliografia
  • [1] D.V. Alekseevsky, C. Medori, A. Tomassini, Homogeneous para-Kähler Einstein manifolds, Russian Math. Surveys, 64(2009), 1–43.[Crossref][WoS]
  • [2] A. Andrada, M.L. Barberis, I.G. Dotti, G. Ovando, Product structures on four-dimensional solvable Lie algebras, Homology,Homotopy and Applications, 7 (2005), 9–37.
  • [3] P. Baird and L. Danielo, Three-dimensional Ricci solitons which project to surfaces, J. Reine Angew.Math., 608 (2007), 65–91.[WoS]
  • [4] N. Blazić, S. Vukmirović, Four-dimensional Lie algebras with a para-hypercomplex structure, Rocky Mountain J. Math., 40(2010), 1391–1439.
  • [5] M. Brozos-Vazquez, G. Calvaruso, E. Garcia-Rio and S. Gavino-Fernandez, Three-dimensional Lorentzian homogeneous Riccisolitons, Israel J. Math., 188 (2012), 385–403.
  • [6] G. Calvaruso, Symplectic, complex and Kähler structures on four-dimensional generalized symmetric spaces, Diff. Geom.Appl., 29 (2011), 758–769.[Crossref]
  • [7] G. Calvaruso, Four-dimensional paraKähler Lie algebras: classification and geometry, Houston J. Math., to appear.
  • [8] G. Calvaruso and A. Fino, Complex and paracomplex structures on homogeneous pseudo-Riemannian four-manifolds, Int. J.Math., 24 (2013), 1250130, 28 pp.[Crossref][WoS]
  • [9] G. Calvaruso and A. Fino, Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces, Canad. J.Math., 64 (2012), 778–804.
  • [10] G. Calvaruso and A. Fino, Four-dimensional pseudo-Riemannian homogeneous Ricci soliton, Arxiv: 1111.6384. To appear inInt. J. Geom. Methods Mod. Phys.[WoS]
  • [11] H.-D. Cao, Recent progress on Ricci solitons, Recent advances in geometric analysis, 1–38, Adv. Lect. Math. (ALM), 11, Int.Press, Somerville, MA, 2010.
  • [12] V. Cruceanu, P. Fortuny and P.M. Gadea, A survey on paracomplex geometry, Rocky Mount. J. Math., 26 (1996), 83–115.
  • [13] B.Y. Chu, Symplectic homogeneous spaces, Trans. Amer. Math. Soc., 197 (1974), 145–159.
  • [14] A.S. Dancer and M.Y. Wang, Some new examples on non-Ka¨ hler Ricci solitons, Math. Res. Lett., 16 (2009), no. 2, 349–363.[Crossref]
  • [15] A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata, 7 (1978), 259–280.
  • [16] J. Lauret, Ricci solitons solvmanifolds, J. Reine Angew. Math., 650 (2011), 1–21.
  • [17] G. Ovando, Invariant complex structures on solvable real Lie groups, Manuscripta Math., 103, (2000), 19–30.
  • [18] G. Ovando, Four-dimensional symplectic Lie algebras, Beiträge Algebra Geom., 47(2006), no. 2, 419–434.
  • [19] G. Ovando, Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory, 16 (2006), 371–391.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_coma-2015-0001
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