Eberlein, Patrick Isometry groups of simply connected manifolds of nonpositive curvature. II. (English) Zbl 0511.53048 Acta Math. 149, 41-69 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 20 Documents MSC: 53C20 Global Riemannian geometry, including pinching 53C35 Differential geometry of symmetric spaces Keywords:duality condition; Selberg property; density properties; group of isometries; Riemannian symmetric spaces Citations:Zbl 0094.249; Zbl 0413.53029; Zbl 0401.53015 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Ballmann, W.,Einige neue resultate über Mannigfaltigkeiten negativer Krümmung. Dissertation, Univ. of Bonn, 1978. · Zbl 0421.53032 [2] Ballmann, W.,Einige neue resultate über Mannigfaltigkeiten negativer Krümmung. Bonner Math. Schriften, Vol. 113, 1978. · Zbl 0421.53032 [3] Bishop, R. &O’Neill, B., Manifolds of negative curvature.Trans. Amer. Math. Soc., 145 (1969), 1–49. · Zbl 0191.52002 · doi:10.1090/S0002-9947-1969-0251664-4 [4] Borel, A., Compact Clifford-Klein forms of symmetric spaces.Topology, 2 (1963), 111–122. · Zbl 0116.38603 · doi:10.1016/0040-9383(63)90026-0 [5] –, Density properties for certain subgroups of semi-simple groups without compact components.Ann. of Math., 72(1) (1960), 179–188. · Zbl 0094.24901 · doi:10.2307/1970150 [6] Cartan, E.,Leçons sur la géométrie des espaces de Riemann. Paris, Gauthier-Villars, 1946. · Zbl 0060.38101 [7] –, Sur une classe remarquable d’espaces de Riemann.Bull. Soc. Math. France, 54 (1926), 214–264 and 55 (1927), 114–134. · JFM 52.0425.01 [8] –, Sur certaines formes Riemanniennes remarquables des géométries à group fondamental simple.Ann. École Norm., 44 (1927), 345–467. · JFM 53.0393.01 [9] Cartan, E. Les espaces Riemanniens symétriques.Verh. Int. Math. Kongr., I.Zürich (1932), 152–161. · JFM 58.1253.03 [10] Chen, S., Duality condition and Property (S).Pacific J. Math., 98 (1982), 313–322. · Zbl 0483.53040 [11] Chen, S. &Eberlein, P., Isometry groups of simply connected manifolds of nonpositive curvature.Illinois J. Math., 24 (1) (1980), 73–103. · Zbl 0413.53029 [12] Dani, S. G., A simple proof of Borel’s density theorem.Math. Z., 174 (1980), 81–94. · Zbl 0432.22008 · doi:10.1007/BF01215084 [13] Eberlein, P., Geodesic flows on negatively curved manifolds, I.Ann. of Math., 95 (1972), 492–510. · Zbl 0217.47304 · doi:10.2307/1970869 [14] –, Geodesic flows on negatively curved manifolds, II.Trans. Amer. Math. Soc., 178 (1973), 57–82. · Zbl 0264.53027 · doi:10.1090/S0002-9947-1973-0314084-0 [15] –, Lattices in spaces of nonpositive curvature.Ann. of Math., 111 (1980), 435–476. · doi:10.2307/1971104 [16] Eberlein, P. &O’Neill, B., Visibility manifolds.Pacific J. Math., 46 (1973), 45–109. · Zbl 0264.53026 [17] Goto, M. &Goto, M., Isometry groups of negatively pinched 3-manifolds.Hiroshima Math. J., 9 (2) (1979), 313–319. · Zbl 0496.53029 [18] Gromoll, D. &Wolf, J., 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. · Zbl 0237.53037 · doi:10.1090/S0002-9904-1971-12747-7 [19] Heintze, E., Personal communication. [20] Heintze, E.,Mannigfaltigkeiten negativer Krümmung. Habilitationschrift, University of Bonn, 1976. [21] Helgason, S.,Differential geometry and symmetric spaces. Academic Press, New York, 1962. · Zbl 0111.18101 [22] Kobayashi, S., Fixed points of isometries.Nagoya Math. J., 13 (1958), 63–68. · Zbl 0084.18202 [23] –,Transformation groups in differential geometry. Springer-Verlag, New York, 1972. · Zbl 0246.53031 [24] Kobayashi, S. &Nomizu, K.,Foundations of differential geometry, Vol. 1. J. Wiley and Sons, New York, 1963, pp. 179–193. · Zbl 0119.37502 [25] Lawson, H. B. &Yau, S.-T., Compact manifolds of nonpositive curvature,J. Differential Geom., 7 (1972), 211–228. · Zbl 0266.53035 [26] Mostow, G. D.,Strong rigidity of locally symmetric spaces. Annals of Math. Studies, number 78. Princeton University Press, Princeton, New Jersey, 1973. · Zbl 0265.53039 [27] Raghunathan, M. S.,Discrete subgroups of Lie groups. Springer-Verlag, New York, 1972. · Zbl 0254.22005 [28] Shimizu, H., On discontinuous groups operating on the product of upper half planes.Ann. of Math., 77 (1) (1963), 33–71. · Zbl 0218.10045 · doi:10.2307/1970201 [29] Wolf, J., Homogeneity and bounded isometries in manifolds of negative curvature.Illinois J. Math., 8 (1964), 14–18. · Zbl 0126.17702 [30] Wolf, J.,Spaces of constant curvature. 2nd edition, published by the author. Berkeley, California, 1972. · Zbl 0234.33012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. 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