Skip to main content
Log in

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

Access this article

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

Instant access to the full article PDF.

References

  1. W. Ballmann:Einige neue resultate über Mannigfaltigkeiten negativer Krümmung, dissertation, Univ. of Bonn, 1978 and Bonner Math. Schriften, vol. 113, 1978.

  2. R. Bishop and R. CrittendenGeometry of Manifolds, Academic Press, New York, NY, 1964.

    MATH  Google Scholar 

  3. Bishop and B. O'Neill:Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Berger, P. Gauduchon and E. Mazet;Le Spectre d'une Variété Riemannienne, Springer-Verlag, vol. 194, New York, 1971.

    MATH  Google Scholar 

  5. R. Cahn, P. Gilkey and J. Wolf, “Heat equation, proportionality principle and volume of fundamental domains”, Differential Geometry and Relativity, D. Reidel Pub. Co., 1976, 43–54.

  6. C. Chabauty:Limite d'ensembles et géométrie des nombres, Bull. Soc. Math. France, 78 (1950), 143–151.

    MATH  MathSciNet  Google Scholar 

  7. S. Chen;Spectra of discrete uniform subgroups of semisimples Lie groups, Math. Ann. 237 (1978), 157–159.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Chen;Duality condition and property (S), preprint, 1980.

  9. S. Chen and P. Eberlein:Isometry groups of simply connected manifolds of nonpositive curvature, Ill. J. Math. 24 (1) (1980), 73–103.

    MATH  MathSciNet  Google Scholar 

  10. S. S. Chern, “On curvature and characteristic classes of a Riemann manifold”, Abh. Math. Sem. Hamburg 20 (1955), 117–126.

    MATH  MathSciNet  Google Scholar 

  11. P. Eberlein,Isometry groups of simply connected manifolds of nonpositive curvature, II, to apear in Acta Mathematica.

  12. —,Lattices in spaces of nonpositive curvature, Annals of Math., 111 (1980). 435–476.

    Article  MathSciNet  Google Scholar 

  13. P. Eberlein and B. O'Neill:Visibility manifolds, Pac. J. Math. 46 (1973), 45–109.

    MATH  MathSciNet  Google Scholar 

  14. M. Gromov:Hyperbolic manifolds according to Thurston and Jørgensen, Seminaire Bourbaki, Number 546, 1979/80.

  15. —,Manifolds of negative curvature, J. Diff. Geom. 13 (1978), 223–230.

    MATH  MathSciNet  Google Scholar 

  16. W. Harvey,Discrete Groups and Automorphic Functions, Academic Press, London, 1977.

    MATH  Google Scholar 

  17. E. Heintze:Mannigfaltigkeiten negativer Krümmung, Habilitationsschrift, Univ. of Bonn. 1976.

  18. S. Helgason;Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.

    MATH  Google Scholar 

  19. F. Hirzebruch, “Automorphe Formen und der Satz von Riemann-Roch”, Symposium Internacional de Topologia Algebraica, Mexico City, 1958, 129–144.

  20. A. D. Kazdan and G. A. Margulis:A proof of Selberg's hypothesis, Mat. Sb., (117), 75 (1968), 163–168.

    MathSciNet  Google Scholar 

  21. S. Kobayashi and K. Nomizu;Foundations of Differential Geometry, Vol. 1, J. Wiley and Sons, New York, 1963, pp. 179–193.

    MATH  Google Scholar 

  22. H. B. Lawson and S.-T. Yau;Compact manifolds of nonpositive curvature, J. Diff. Geom. 7 (1972), 211–228.

    MATH  MathSciNet  Google Scholar 

  23. A. M. Macbeath;Groups of homeomorphisms of a simply connected space, Annals of Math. (2) 79 (1964), 473–488.

    Article  MathSciNet  Google Scholar 

  24. G. A. Margulis;Discrete groups of motions of manifolds of nonpositive curvature, Amer. Math. Soc. Transl. (2) Vol. 109 (1977), 32–45.

    MathSciNet  Google Scholar 

  25. H. P. McKean:Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246.

    MathSciNet  Google Scholar 

  26. G. D. Mostow,Strong Rigidity of Locally Symmetric Spaces, Annals of Math. Studies 78, Princeton Univ. Press, Princenton, 1973.

    MATH  Google Scholar 

  27. D. Mumford;A remark on Mahler's compactness theorem, Proc. Amer. Math; Soc. 28 (1971), 289–294.

    Article  MATH  MathSciNet  Google Scholar 

  28. M. S. Raghunathan;Discrete Subgroups of Lie Groups, Springer-Verlag, New York, 1972.

    MATH  Google Scholar 

  29. T. Sunada,Spectrum of a compact flat manifold, Comment. Math. Helv. 53 (1978) 613–621.

    Article  MATH  MathSciNet  Google Scholar 

  30. W. Thurston;The Geometry and Topology of 3-manifolds, Lecture notes from Princenton Univ., 1977/78.

  31. H.-C. Wang;Topics in totally discontinuous groups, inSymmetric Spaces…, edited by W. Boothby and G. Weiss, Marcel Dekker, 1972, pp. 460–485.

  32. A. WeilOn discrete subgroups of Lie groups, Ann. of Math. 72 (1960), 369–384; and 75 (1962), 578–602.

    Article  MathSciNet  Google Scholar 

  33. J. Wolf,Homogeneity and bounded isometries in manifolds of negative curvature, Ill. J. Math. 8 (1964), 14–18.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by NSF Grant MCS-7901730.

About this article

Cite this article

Chen, SS., Eberlein, P. Isometry classes of lattices of nonpositive curvature and uniformly bounded volume. Bol. Soc. Bras. Mat 13, 25–44 (1982). https://doi.org/10.1007/BF02584733

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02584733

Keywords

Navigation