Codimension one tori in manifolds of nonpositive curvature
- 45 Downloads
A complete Riemannian manifold of nonpositive sectional curvature and finite volume contains a totally geodesic flat torus of codimension one provided it contains a codimension one flat.
KeywordsRiemannian Manifold Finite Volume Sectional Curvature Complete Riemannian Manifold Nonpositive Curvature
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 1.Ballmann, W., ‘Axial Isometries of Manifolds of Nonpositive Curvature’, Math. Ann. 259 (1982), 131–144.Google Scholar
- 2.Ballmann, W., Gromov, M. and Schroeder, V., ‘Manifolds of Nonpositive Curvature’, Basel, Boston, 1985.Google Scholar
- 3.Bangert, V. and Schroeder, V., ‘Existence of Flat Tori in Analytic Manifolds of Nonpositive Curvature’, Preprint, Bern-Münster, 1989.Google Scholar
- 4.Bishop, R. and O'Neill, B., ‘Manifolds of Negative Curvature’, Trans. A.M.S. 145 (1969), 1–49.Google Scholar
- 5.Buyalo, S. V., ‘Euclidean Planes in Three-Dimensional Manifolds of Nonpositive Curvature’, Mat. Zametki 43 (1988), 103–114, translated in Math. Notes 43(1988), 60–66.Google Scholar
- 6.Eberlein, P., ‘Euclidean de Rham Factor of a Lattice of Nonpositive Curvature’, J. Diff. Geom. 18 (1983), 209–220.Google Scholar
- 7.Eberlein, P. and O'Neill, B., ‘Visibility Manifolds’, Pacific J. Math. 46 (1973), 45–109.Google Scholar
- 8.Gromoll, D. and Wolf, J., ‘Some Relations between the Metric Structure and the Algebraic Structure of the Fundamental Group in Manifolds of Nonpositive Curvature; Bull. A.M.S. 77 (1971), 545–552.Google Scholar
- 9.Gromov, M., ‘Manifolds of Negative Curvature’, J. Diff. Geom. 13 (1978), 223–230.Google Scholar
- 10.Lawson, H. B. and Yau, S. T., ‘Compact Manifolds of Nonpositive Curvature’, J. Diff. Geom. 7 (1972), 211–228.Google Scholar
- 11.Schroeder, V., ‘Existence of Immersed Tori in Manifolds of Nonpositive Curvature’, J. reine angew. Math. 390 (1988), 32–46.Google Scholar
- 12.Schroeder, V., ‘Structure of Flat Subspaces in Low Dimensional Manifolds of Nonpositive Curvature’, Manuscripta Math. 64 (1989), 77–105.Google Scholar
© Kluwer Academic Publishers 1990