The isometry groups of Lorentzian three-dimensional unimodular simply connected Lie groups

Authors

  • Mohamed Boucetta Université Cadi Ayyad, Faculté des sciences et techniques, B.P. 549, Marrakech, Maroc
  • Abdelmounaim Chakkar Université Cadi Ayyad, Faculté des sciences et techniques, B.P. 549, Marrakech, Maroc

DOI:

https://doi.org/10.33044/revuma.2021

Abstract

We determine the isometry groups of all three-dimensional, connected, simply connected and unimodular Lie groups endowed with a left-invariant Lorentzian metric.

Downloads

Download data is not yet available.

References

M. Boucetta and A. Chakkar, The moduli spaces of Lorentzian left-invariant metrics on three-dimensional unimodular simply connected Lie groups, J. Korean Math. Soc. 59 (2022), no. 4, 651–684. MR 4446209.

P. Bueken and M. Djorić, Three-dimensional Lorentz metrics and curvature homogeneity of order one, Ann. Global Anal. Geom. 18 (2000), no. 1, 85–103. MR 1739527.

G. Calvaruso, Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds, Geom. Dedicata 127 (2007), 99–119. MR 2338519.

L. A. Cordero and P. E. Parker, Isometry groups of pseudoriemannian 2-step nilpotent Lie groups, Houston J. Math. 35 (2009), no. 1, 49–72. MR 2491866.

V. del Barco and G. P. Ovando, Isometric actions on pseudo-Riemannian nilmanifolds, Ann. Global Anal. Geom. 45 (2014), no. 2, 95–110. MR 3165476.

S. Dumitrescu and A. Zeghib, Géométries lorentziennes de dimension 3: classification et complétude, Geom. Dedicata 149 (2010), 243–273. MR 2737692.

K. Y. Ha and J. B. Lee, Left invariant metrics and curvatures on simply connected three-dimensional Lie groups, Math. Nachr. 282 (2009), no. 6, 868–898. MR 2530885.

K. Y. Ha and J. B. Lee, The isometry groups of simply connected 3-dimensional unimodular Lie groups, J. Geom. Phys. 62 (2012), no. 2, 189–203. MR 2864471.

A. Krasiński, C. G. Behr, E. Schücking, F. B. Estabrook, H. D. Wahlquist, G. F. R. Ellis, R. Jantzen and W. Kundt, The Bianchi classification in the Schücking-Behr approach, Gen. Relativity Gravitation 35 (2003), no. 3, 475–489. MR 1964375.

J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 0425012.

D. Müller, Isometries of bi-invariant pseudo-Riemannian metrics on Lie groups, Geom. Dedicata 29 (1989), no. 1, 65–96. MR 0989188.

B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, New York, 1983. MR 0719023.

T. Šukilović, Geometric properties of neutral signature metrics on 4-dimensional nilpotent Lie groups, Rev. Un. Mat. Argentina 57 (2016), no. 1, 23–47. MR 3519282.

F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, corrected reprint of the 1971 edition, Graduate Texts in Mathematics, 94, Springer-Verlag, New York, 1983. MR 0722297.

Downloads

Published

2022-09-28