Fundamental groups of manifolds of nonpositive curvature

作者: Werner Ballmann , Patrick Eberlein

DOI: 10.4310/JDG/1214440722

关键词: Riemannian manifoldRank (differential topology)MathematicsSymmetric spaceSectional curvatureScalar curvatureMathematical analysisCovering spacePure mathematicsCurvatureFundamental group

摘要: … Riemannian manifold M of nonpositive sectional curvature is … (1) the sectional curvature is nonpositive and bounded from … Manifolds of rank one resemble manifolds of strictly negative …

参考文章(16)
M. S. Raghunathan, Discrete subgroups of Lie groups ,(1972)
Patrick Eberlein, Euclidean de Rham factor of a lattice of nonpositive curvature Journal of Differential Geometry. ,vol. 18, pp. 209- 220 ,(1983) , 10.4310/JDG/1214437661
H. Blaine Lawson, Jr., Shing Tung Yau, Compact manifolds of nonpositive curvature Journal of Differential Geometry. ,vol. 7, pp. 211- 228 ,(1972) , 10.4310/JDG/1214430828
Su-Shing Chen, Patrick Eberlein, Isometry groups of simply connected manifolds of nonpositive curvature Illinois Journal of Mathematics. ,vol. 24, pp. 73- 103 ,(1980) , 10.1215/IJM/1256047798
M. Gromov, Manifolds of negative curvature Journal of Differential Geometry. ,vol. 13, pp. 223- 230 ,(1978) , 10.4310/JDG/1214434487
Gopal Prasad, M. S. Raghunathan, Cartan Subgroups and Lattices in Semi-Simple Groups The Annals of Mathematics. ,vol. 96, pp. 296- ,(1972) , 10.2307/1970790
Patrick Eberlein, Lattices in spaces of nonpositive curvature Annals of Mathematics. ,vol. 111, pp. 435- ,(1980) , 10.2307/1971104
Viktor Schroeder, A splitting theorem for spaces of nonpositive curvature Inventiones Mathematicae. ,vol. 79, pp. 323- 327 ,(1985) , 10.1007/BF01388977
J Tits, Free subgroups in linear groups Journal of Algebra. ,vol. 20, pp. 250- 270 ,(1972) , 10.1016/0021-8693(72)90058-0