References

1
F. Barnet, On Lie groups that admit left-invariant Lorentz metrics of constant sectional curvature, Ill. J. Math. 33 (1989) 631--642.

2
J. Beem, R. Low, and P. Parker, Spaces of Geodesics: Products, Coverings, Connectedness, Geometriae Dedicata 59 (1996) 51--64.

3
J. Bolyai, The science of absolute space, appendix in W. Bolyai, Tentamen Juventutem. Budapest: private, 1832--33.

4
L.A. Cordero and P.E. Parker, Left-invariant Lorentzian metrics on 3-dimensional Lie groups, Rend. Mat. Appl. 17 (1997) 129--155.

5
D. DeTurck and C. Gordon, Isospectral deformations. I, Riemannian structures on two-step nilspaces, Comm. Pure Appl. Math. 40 (1987) 367--387.

6
L. Del Riego and P.E. Parker, Pseudoconvex and disprisoning homogeneous sprays, Geom. Dedicata 55 (1995) 211--220.

7
P. Eberlein, Geometry of 2-step nilpotent groups with a left invariant [sic] metric, Ann. scient. Éc. Norm. Sup. 27 (1994) 611--660.

8
C.F. Gauss, diary entries and letters published posthumously in Werke, vol.8. Leipzig: B.G. Teubner, 1900. pp.157--268 passim.

9
F. Klein, Vergleichende Betrachtungen über neuerer geometrische Forschungen, Math. Ann. 43 (1893) 63--100.

10
J.H. Lambert, Theorie der Parallellinien, Mag. reine angew. Math. (1786) 137--164, 325--358.

11
N.I. Lobachevsky, Géométrie imaginaire, J. für Math. 17 (1837) 295--320.

12
M. Mast, Closed geodesics in 2-step nilmanifolds, Indiana Univ. Math. J. 43 (1994) 885--911.

13
J. Milnor, Curvatures of left invariant [sic] metrics on Lie groups, Adv. in Math. 21 (1976) 293--329.

14
K. Nomizu, Left-invariant Lorentz metrics on Lie groups, Osaka J. Math. 16 (1979) 143--150.

15
G.F.B. Riemann, Über die Hypothesen, welche der Geometrie zu Grunde liegen, Abh. Ges. Wiss. Gött. 13 (1868) 1--20.

16
F.K. Schweikart, memorandum of 1816 sent to Gauß in 1818, unpublished.

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