Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A cusp closing theorem


Author: Viktor Schroeder
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BBE] W. Ballmann, M. Brin, and P. Eberlin, Structure of manifolds of nonpositive curvature. I, Ann. of Math. (2) 122 (1985), 171-203. MR 799256 (87c:58092a)
  • [BGS] W. Ballmann, M. Gromov and V. Schroeder, Manifolds of nonpositive curvature, Birkhäuser, Basel-Boston, 1985. MR 823981 (87h:53050)
  • [BG] K. Burns and M. Gerber, Real analytic Bernoulli geodesic flows on $ {S^2}$, Indiana Univ., preprint.
  • [BO] R. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. MR 0251664 (40:4891)
  • [G] M. Gromov, Hyperbolic manifolds according to Thurston and Jø rgensen, Sém. Bourbaki 546 (1979), Springer Lecture Notes in Math. 842, 40-53. MR 636516 (84b:53046)
  • [S] V. Schroeder, Existence of immersed tori in manifolds of nonpositive curvature, J. Reine Angew. Math., 390 (1988), 32-46. MR 953675 (89i:53032)
  • [T] W. Thurston, The geometry and topology of $ 3$-manifolds, Lecture Notes, Princeton Univ., 1977/78.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20, 53C22, 58F17

Retrieve articles in all journals with MSC: 53C20, 53C22, 58F17


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0957267-6
Keywords: Nonpositive curvature, rank, analytic Riemannian metric
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society