A cusp closing theorem
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- by Viktor Schroeder
- Proc. Amer. Math. Soc. 106 (1989), 797-802
- DOI: https://doi.org/10.1090/S0002-9939-1989-0957267-6
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Abstract:
Using a modification of a cusp closing result of Thurston, we construct compact Riemannian manifolds of nonpositive sectional curvature which have rank one (in the sense of Brin, Ballmann, and Eberlein) but which contain embedded flat tori of codimension 2. The metric can even be made analytic.References
- Werner Ballmann, Misha Brin, and Patrick Eberlein, Structure of manifolds of nonpositive curvature. I, Ann. of Math. (2) 122 (1985), no. 1, 171–203. MR 799256, DOI 10.2307/1971373
- Werner Ballmann, Mikhael Gromov, and Viktor Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics, vol. 61, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 823981, DOI 10.1007/978-1-4684-9159-3 K. Burns and M. Gerber, Real analytic Bernoulli geodesic flows on ${S^2}$, Indiana Univ., preprint.
- 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
- Michael Gromov, Hyperbolic manifolds (according to Thurston and Jørgensen), Bourbaki Seminar, Vol. 1979/80, Lecture Notes in Math., vol. 842, Springer, Berlin-New York, 1981, pp. 40–53. MR 636516
- Viktor Schroeder, Existence of immersed tori in manifolds of nonpositive curvature, J. Reine Angew. Math. 390 (1988), 32–46. MR 953675, DOI 10.1515/crll.1988.390.32 W. Thurston, The geometry and topology of $3$-manifolds, Lecture Notes, Princeton Univ., 1977/78.
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 797-802
- MSC: Primary 53C20; Secondary 53C22, 58F17
- DOI: https://doi.org/10.1090/S0002-9939-1989-0957267-6
- MathSciNet review: 957267