Abstract
In the following paper we classify the connected flat homogeneous spacesM of metric signature (n, 2) with translationally isotropic associated domain.U ⊃IR ns whereIR ns denotesIR n with the usual flat metric istranslationally isotropic if the set of all translations which leaveU invariant contains its perpendicular space. IfU is the image of the universal cover ofM under the development map thenU is called theassociated domain ofM.
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References
Duncan, D.; Ihrig, E.: Homogeneous spacetimes of zero curvature.Proc. Amer. Math. Soc., Nov. 1989.
Duncan, D.;Ihrig, E.: Flat pseudo-Riemannian manifold with a nilpotent transitive group of isometries.Ann. Global Anal. Geom. 10 (1992) 1, 87–101.
Goldman, W.;Hirsch, M.: Affine manifolds and orbits of algebraic groups.Trans. Amer. Math. Soc. 295 (1986), 175–198.
Fried, D.;Goldman, W.;Hirsch, M.: Affine manifolds with nilpotent holonomy.Comment. Math. Helv. 56 (1981), 487–523.
Wolf, J.: Homogeneous manifolds of zero curvature.Trans. Amer. Math. Soc. 104 (1962), 462–469.
Wolf, J.:Spaces of Constant Curvature, McGraw-Hill, New York 1967.
Wolf, J.: Isotropic manifolds of indefinite metric.Comment. Math. Helv. 39 (1964), 21–64.
Yagi, K.: On compact homogeneous affine manifolds.Oskaka J. Math. 7 (1970), 457–475.