Abstract
Flat pseudo-Riemannian manifolds with a nilpotent transitive group of isometries are shown to be complete. Also flat pseudo-Riemannian homogeneous manifolds with non-trivial holonomy are shown to contain a complete geodesic.
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References
Borel, A.: Linear algebraic groups. Benjamin, New York 1969.
Duncan, D.; Ihrig, E.: Homogeneous spacetimes of zero curvature. Proc. A.M.S. 104 (1989), 785–795.
Goldman, W.; Hirsch, M.: Affine manifolds and orbits of algebraic groups. Trans. A.M.S. 295 (1986), 175–198.
Northcott, D.: Affine sets and affine groups. Cambridge 1980.
Rosenlicht, M.: On quotient varieties and the affine embedding of certain homogeneous spaces. Trans. A.M.S. 101 (1961), 211–233.
Scheuneman, J.: Translations in certain groups of affine motions. Proc. A.M.S. 47 (1975), 223–228.
Shimizu, S.: A remark on homogeneous convex domains. Nagoya Math. J. 105 (1987), 1–7.
Vinberg, E.: The theory of convex homogeneous cones. Trans. Moscow Math. Soc. 12(1963), 340–403
Vinberg, E.: The structure of the group of automorphisms of a homogeneous convex cone. Trans. Moscow Math. Soc. 13 (1965), 63–93.
Wolf, J.: Homogeneous manifolds of zero curvature. Trans. A.M.S. 104(1962), 462–469.
Wolf, J.: Isotropic manifolds of indefinite metric. Comment. Math. Helv. 39(1964), 21–64.
Wolf, J.: Spaces of constant curvature. McGraw-Hill, New York 1967.
Yagi, K.: On compact homogeneous affine manifolds. Osaka J. Math. 7(1970), 457–475.
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Duncan, D.C., Ihrig, E.C. Flat Pseudo-Reimannian manifolds with a nilpotent transitive group of isometries. Ann Glob Anal Geom 10, 87–101 (1992). https://doi.org/10.1007/BF00128341
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DOI: https://doi.org/10.1007/BF00128341