Bibliography
Arrowsmith, D. andFurness, P.,Locally symmetric spaces, J. London Math. Soc. (2)10 (1975), 487–499.
—Flat affine Klein bottles, Geometriae Dedicata5 (1976), 109–115.
Atiyah, M. andWall, C.,Cohomology of groups, inAlgebraic Number Theory, Cassels and Frohlich (Eds), 94–115, Thompson Book Co. 1967.
Auslander, L.,Examples of locally affine spaces, Annals of Math.64 (1956), 255–259.
—,An exposition of the theory of solvmanifolds, Bull. Amer. Math. Soc.79 (1973), 227–285.
—,Simply transitive groups of affine matrices, Amer. J. Math.99 (1977), 809–821.
—,Some compact solvmanifolds and locally affine spaces, J. Math. and Mech.7 (1958), 963–975.
—,The structure of complete locally affine manifolds, Topology3 (1964), 131–139.
Auslander, L. andMarkus, L.,Holonomy of flat affinely connected manifolds, Annals of Math.62 (1955), 139–151.
Auslander, L.,Flat Lorentz 3-manifolds, Memoirs Amer. Math. Soc. 1959.
Fillmore, J. andScheuneman, J.,Fundamental groups of compact complete locally affine surfaces, Pacific J. Math.44 (1973), 487–496.
Fried, D.,Polynomials on affine manifolds. To appear.
Fried, D. andGoldmann, W., 3-dimensional affine crystallographic groups. To appear.
Goldman, W. andHirsch, M.,Polynomial forms on affine manifolds, Pacific J. Math. (in press).
Furness, P. andFedida, E.,Sur les structures pseudo-riemanniennes plates des variétés compactes, C.R. Acad. Sci, Paris,286 (1978), 1969–171.
Goldman, W.,Obstructions to deforming geometric structures, to appear.
Goldman, W.,Two examples of affine manifolds, to appear.
Goldmann, W. andHirsch, M.,A generalization of Bieberbach's theorem, Invent. Math. (in press).
Gunning, R.,Uniformization of complex manifolds: the role of connections, Princeton U. Press, 1978.
Hirsch, M.,Flat manifolds and the cohomology of groups, inAlgebraic and geometric topology, Lecture Notes in Mathematics 664, Springer-Verlag, 1977.
—,Stability of stationary points and cohomology of groups, Proc. Amer. Math. Soc.79 (1980) 191–196.
Hirsch, M. andThurston, W.,Foliated bundles, flat manifolds, and invariant measures, Annals of Math.101 (1975), 369–390.
Humphreys, J.,Linear algebraic groups, Springer-Verlag, 1975.
Inoue, M., Kobayashi, S. andOchiai, T.,Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. U. Tokyo27 (1980), 247–264.
Kostant, B. andSullivan, D.,The Euler characteristic of an affine space form is zero, Bull. Amer. Math. Soc.81 (1975), 937–938.
Kuiper, N.,Sur les surfaces localement affines, Colloques de géométrie différentielle, Strasbourg (1953), 79–87.
Malcev, A. On a class of homogeneous spaces, Izvestija Akademia Nauk SSR Ser. Math.13 (1949); Amer. Math. Soc. Translations9 (1962), 276–307.
Markus, L.,Cosmological models in differential geometry, U. Minnesota 1962 (mimeographed).
Matsushima, Y.,Affine structures on complex manifolds, Osaka J. Math.5 (1968), 215–222.
Milnor, J.,Curvatures of left-invariant metrics on Lie groups, Adv. in Math.21 (1976), 293–329.
—,On fundamental groups of complete affinely flat manifolds, Adv. in Math.25 (1977), 178–187.
Nagano, T. andYagi, K.,The affine structures on the real two-torus I, Asapa J. Math.11 (1974), 181–210.
Nomizu, K.,On the cohomology ring of compact homogeneous spaces of nilpotent Lie groups, Annals of Maths.59 (1954), 531–538.
Sakane, Y.,On compact complex affine manifolds, J. Math. Soc. Japan29 (1977), 135–145.
Scheuneman, J.,Examples of compact locally affine spaces, Bull. Amer. Math. Soc.77 (1974), 589–592.
—,Affine structures on three-step nilpotent Lie algebras, Proc. Amer. Math. Soc.46 (1974), 451–454.
—,Translations in certain groups of affine motions, Proc. Amer. Math. Soc.47 (1975), 223–228.
Smillie, J.,Affinely flat manifolds, Doctoral thesis, U. Chicago (1977).
Sullivan, D.,A generalization of Milnor's inequality concerning affine foliations and affine manifolds, Comment. Math. Helv.51 (1976), 183–189.
Sullivan, D. andThurston, W.,Manifolds with canonical coordinates: some examples. Institut des Hautes Etudes, 1979, mimeographed.
Suwa, T.,Compact quotient spaces of C 2 by affine transformation groups, J. Diff. Geom.10 (1975), 239–252.
Tischler, D.,On fibering certain foliated manifolds over S 1, Topology9 (1970), 153–154.
Varadarajan, V.,Lie groups, Lie algebras, and their representations, Printice Hall, 1974.
Vitter, A.,Affine structures on compact complex manifolds, Invent. Math.17 (1972), 231–244.
Zassenhaus, H.,Beweis eines Satzes über diskrete Gruppen, Abhandl. Math. Sem. Univ. Hamburg12 (1938), 289–312.
Dwyer, W. G.,Vanishing homology over nilpotent groups, Proc. Amer. Math. Soc.49 (1975), 8–12.
Raghunathan, M. S. Discrete subgroups of Lie groups, Springer-Verlag 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fried, D., Goldman, W. & Hirsch, M.W. Affine manifolds with nilpotent holonomy. Commentarii Mathematici Helvetici 56, 487–523 (1981). https://doi.org/10.1007/BF02566225
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02566225