Isometry groups of manifolds of negative curvature

Byers, W.

doi:10.1090/S0002-9939-1976-0390960-6

Isometry groups of manifolds of negative curvature
HTML articles powered by AMS MathViewer

by W. Byers

Proc. Amer. Math. Soc. 54 (1976), 281-285

DOI: https://doi.org/10.1090/S0002-9939-1976-0390960-6

PDF | Request permission

Abstract:

Solvable subgroups of the isometry groups of a simply-connected manifold of negative curvature are characterized and this characterization is used to show that the isometry group of the universal Riemannian covering of a compact manifold of negative curvature is either discrete or semisimple.

References

V. I. Arnold and A. Avez, Problèmes ergodiques de la mécanique classique, Monographies Internationales de Mathématiques Modernes, vol. 9, Gauthier-Villars, Éditeur, Paris, 1967 (French). MR 0209436
R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49. MR 251664, DOI 10.1090/S0002-9947-1969-0251664-4
P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. MR 336648
Detlef Gromoll and Joseph A. Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77 (1971), 545–552. MR 281122, DOI 10.1090/S0002-9904-1971-12747-7
Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Alexandre Preissmann, Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv. 15 (1943), 175–216 (French). MR 10459, DOI 10.1007/BF02565638
Shing-tung Yau, On the fundamental group of compact manifolds of non-positive curvature, Ann. of Math. (2) 93 (1971), 579–585. MR 283726, DOI 10.2307/1970888

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 54 (1976), 281-285
DOI: https://doi.org/10.1090/S0002-9939-1976-0390960-6
MathSciNet review: 0390960