Homogeneous Lorentzian Spaces Whose Null-geodesics are Canonically Homogeneous
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Abstract
It is shown that a homogeneous Lorentzian space for which every null-geodesic is canonically homogeneous, admits a non-vanishing homogeneous Lorentzian structure belonging to the class \(\mathcal{T}_{1}\oplus\mathcal{T}_{3}\).
Mathematics Subject Classifications (2000)
22F30 53C22 53C50Keywords
Homogeneous spaces null-geodesics Lorentzian signaturePreview
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References
- 1.Kowalski O., Szenthe On the existence of homogeneous geodesics in homogeneous Riemannian manifolds. Geom. Dedicata 81, 209–214 (2000) Erratum: ibid 84, 331–332 (2001)Google Scholar
- 2.Philip, S.: Penrose limits of homogeneous spaces. math.DG/0405506Google Scholar
- 3.Kowalski O., Vanhecke L. (1991) Riemannian manifolds with homogeneous geodesics. Boll. Unione Mat. Ital. 5-B, 189–246MathSciNetGoogle Scholar
- 4.Figueroa-O’Farrill, J., Meessen, P., Philip, S.: Homogeneity and plane-wave limits. J. High Energy Phys. 0505 050 (2005) (hep-th/0504069)Google Scholar
- 5.Ambrose W., Singer I.M. (1958) On homogeneous Riemannian manifolds. Duke Math. J. 25: 647–669CrossRefMATHMathSciNetGoogle Scholar
- 6.Tricerri F., Vanhecke L. (1983). Homogeneous structures on Riemannian manifolds. London Math. Soc. Lecture Note Ser. 83, 1–125MathSciNetGoogle Scholar
- 7.Meessen P. (2006) Lorentzian homogeneous spaces admitting a homogeneous structure of type \(\mathcal{T}_{1}\oplus\mathcal{T}_{3}\), J. Geom. Phys. 56, 754–761CrossRefMATHADSMathSciNetGoogle Scholar
- 8.(math.DG/0504127)Google Scholar
- 9.Blau M., O’Loughlin M. (2003) Homogeneous plane waves. Nuclear Phys. B 654, 135–176 (hep-th/0212135)CrossRefMATHADSMathSciNetGoogle Scholar
- 9.Blau M., O’Loughlin M., Papadopoulos G., Tseytlin A.A. (2003) Solvable models of strings in homogeneous plane wave backgrounds. Nucl. Phys. B 673, 57–97 (hep-th/0304198)CrossRefMATHADSMathSciNetGoogle Scholar
- 10.Kobayashi S., Nomizu K. (1969) Foundations of differential geometry. Wiley, Newyork vol. II.Google Scholar
- 11.Gadea P.M., Oubiña J.A. (1997) Reductive homogeneous pseudo-Riemannian manifolds. Monatsh. Math. 124, 17–34CrossRefMATHMathSciNetGoogle Scholar
- 12.Gadea P.M., Oubiña J.A. (1992) Homogeneous pseudo-Riemannian structures and homogeneous almost para-Hermitian structures. Houston J. Math. 18, 449–465MATHGoogle Scholar
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