Skip to main content
SpringerLink
Log in

Affine manifolds with nilpotent holonomy

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Arrowsmith, D. andFurness, P.,Locally symmetric spaces, J. London Math. Soc. (2)10 (1975), 487–499.

    MathSciNet  MATH  Google Scholar 

  2. —Flat affine Klein bottles, Geometriae Dedicata5 (1976), 109–115.

    Article  MathSciNet  MATH  Google Scholar 

  3. Atiyah, M. andWall, C.,Cohomology of groups, inAlgebraic Number Theory, Cassels and Frohlich (Eds), 94–115, Thompson Book Co. 1967.

  4. Auslander, L.,Examples of locally affine spaces, Annals of Math.64 (1956), 255–259.

    Article  MathSciNet  MATH  Google Scholar 

  5. —,An exposition of the theory of solvmanifolds, Bull. Amer. Math. Soc.79 (1973), 227–285.

    Article  MathSciNet  MATH  Google Scholar 

  6. —,Simply transitive groups of affine matrices, Amer. J. Math.99 (1977), 809–821.

    Article  MathSciNet  MATH  Google Scholar 

  7. —,Some compact solvmanifolds and locally affine spaces, J. Math. and Mech.7 (1958), 963–975.

    MathSciNet  MATH  Google Scholar 

  8. —,The structure of complete locally affine manifolds, Topology3 (1964), 131–139.

    Article  MathSciNet  MATH  Google Scholar 

  9. Auslander, L. andMarkus, L.,Holonomy of flat affinely connected manifolds, Annals of Math.62 (1955), 139–151.

    Article  MathSciNet  MATH  Google Scholar 

  10. Auslander, L.,Flat Lorentz 3-manifolds, Memoirs Amer. Math. Soc. 1959.

  11. Fillmore, J. andScheuneman, J.,Fundamental groups of compact complete locally affine surfaces, Pacific J. Math.44 (1973), 487–496.

    Article  MathSciNet  MATH  Google Scholar 

  12. Fried, D.,Polynomials on affine manifolds. To appear.

  13. Fried, D. andGoldmann, W., 3-dimensional affine crystallographic groups. To appear.

  14. Goldman, W. andHirsch, M.,Polynomial forms on affine manifolds, Pacific J. Math. (in press).

  15. Furness, P. andFedida, E.,Sur les structures pseudo-riemanniennes plates des variétés compactes, C.R. Acad. Sci, Paris,286 (1978), 1969–171.

    MATH  Google Scholar 

  16. Goldman, W.,Obstructions to deforming geometric structures, to appear.

  17. Goldman, W.,Two examples of affine manifolds, to appear.

  18. Goldmann, W. andHirsch, M.,A generalization of Bieberbach's theorem, Invent. Math. (in press).

  19. Gunning, R.,Uniformization of complex manifolds: the role of connections, Princeton U. Press, 1978.

  20. Hirsch, M.,Flat manifolds and the cohomology of groups, inAlgebraic and geometric topology, Lecture Notes in Mathematics 664, Springer-Verlag, 1977.

  21. —,Stability of stationary points and cohomology of groups, Proc. Amer. Math. Soc.79 (1980) 191–196.

    Article  MathSciNet  MATH  Google Scholar 

  22. Hirsch, M. andThurston, W.,Foliated bundles, flat manifolds, and invariant measures, Annals of Math.101 (1975), 369–390.

    Article  MATH  Google Scholar 

  23. Humphreys, J.,Linear algebraic groups, Springer-Verlag, 1975.

  24. Inoue, M., Kobayashi, S. andOchiai, T.,Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. U. Tokyo27 (1980), 247–264.

    MathSciNet  MATH  Google Scholar 

  25. Kostant, B. andSullivan, D.,The Euler characteristic of an affine space form is zero, Bull. Amer. Math. Soc.81 (1975), 937–938.

    Article  MathSciNet  MATH  Google Scholar 

  26. Kuiper, N.,Sur les surfaces localement affines, Colloques de géométrie différentielle, Strasbourg (1953), 79–87.

  27. Malcev, A. On a class of homogeneous spaces, Izvestija Akademia Nauk SSR Ser. Math.13 (1949); Amer. Math. Soc. Translations9 (1962), 276–307.

  28. Markus, L.,Cosmological models in differential geometry, U. Minnesota 1962 (mimeographed).

  29. Matsushima, Y.,Affine structures on complex manifolds, Osaka J. Math.5 (1968), 215–222.

    MathSciNet  MATH  Google Scholar 

  30. Milnor, J.,Curvatures of left-invariant metrics on Lie groups, Adv. in Math.21 (1976), 293–329.

    Article  MathSciNet  MATH  Google Scholar 

  31. —,On fundamental groups of complete affinely flat manifolds, Adv. in Math.25 (1977), 178–187.

    Article  MathSciNet  MATH  Google Scholar 

  32. Nagano, T. andYagi, K.,The affine structures on the real two-torus I, Asapa J. Math.11 (1974), 181–210.

    MathSciNet  MATH  Google Scholar 

  33. Nomizu, K.,On the cohomology ring of compact homogeneous spaces of nilpotent Lie groups, Annals of Maths.59 (1954), 531–538.

    Article  MathSciNet  MATH  Google Scholar 

  34. Sakane, Y.,On compact complex affine manifolds, J. Math. Soc. Japan29 (1977), 135–145.

    Article  MathSciNet  MATH  Google Scholar 

  35. Scheuneman, J.,Examples of compact locally affine spaces, Bull. Amer. Math. Soc.77 (1974), 589–592.

    Article  MathSciNet  MATH  Google Scholar 

  36. —,Affine structures on three-step nilpotent Lie algebras, Proc. Amer. Math. Soc.46 (1974), 451–454.

    Article  MathSciNet  MATH  Google Scholar 

  37. —,Translations in certain groups of affine motions, Proc. Amer. Math. Soc.47 (1975), 223–228.

    Article  MathSciNet  MATH  Google Scholar 

  38. Smillie, J.,Affinely flat manifolds, Doctoral thesis, U. Chicago (1977).

  39. Sullivan, D.,A generalization of Milnor's inequality concerning affine foliations and affine manifolds, Comment. Math. Helv.51 (1976), 183–189.

    Article  MathSciNet  MATH  Google Scholar 

  40. Sullivan, D. andThurston, W.,Manifolds with canonical coordinates: some examples. Institut des Hautes Etudes, 1979, mimeographed.

  41. Suwa, T.,Compact quotient spaces of C 2 by affine transformation groups, J. Diff. Geom.10 (1975), 239–252.

    Article  MATH  Google Scholar 

  42. Tischler, D.,On fibering certain foliated manifolds over S 1, Topology9 (1970), 153–154.

    Article  MathSciNet  MATH  Google Scholar 

  43. Varadarajan, V.,Lie groups, Lie algebras, and their representations, Printice Hall, 1974.

  44. Vitter, A.,Affine structures on compact complex manifolds, Invent. Math.17 (1972), 231–244.

    Article  MathSciNet  MATH  Google Scholar 

  45. Zassenhaus, H.,Beweis eines Satzes über diskrete Gruppen, Abhandl. Math. Sem. Univ. Hamburg12 (1938), 289–312.

    Article  MathSciNet  MATH  Google Scholar 

  46. Dwyer, W. G.,Vanishing homology over nilpotent groups, Proc. Amer. Math. Soc.49 (1975), 8–12.

    Article  MathSciNet  MATH  Google Scholar 

  47. Raghunathan, M. S. Discrete subgroups of Lie groups, Springer-Verlag 1972.

Download references

Author information

Authors and Affiliations

  1. University of California, Santa Cruz

    David Fried, William Goldman & Morris W. Hirsch

  2. University of California, Berkeley

    David Fried, William Goldman & Morris W. Hirsch

  3. University of California, Berkeley

    David Fried, William Goldman & Morris W. Hirsch

Authors
  1. David Fried
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Goldman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Morris W. Hirsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566225

Keywords

Search

Navigation