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)

 
 

 

The Euclidean factor of a Hadamard manifold


Authors: Toshiaki Adachi and Fumiko Ohtsuka
Journal: Proc. Amer. Math. Soc. 113 (1991), 209-212
MSC: Primary 53C20; Secondary 53C23
DOI: https://doi.org/10.1090/S0002-9939-1991-1074746-3
MathSciNet review: 1074746
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The ideal boundary $ X(\infty )$ of a Hadamard manifold $ X$ is the set of asymptotic classes of rays on $ X$. We shall characterize the Euclidean factor of $ X$ by information on $ X(\infty )$. Under the assumption that the diameter of $ X(\infty )$ is $ \pi $, we call a boundary point that has a unique point of Tits distance $ \pi $ a polar point. We shall show that such points form a standard sphere and compose the boundary of the Euclidean factor of the given Hadamard manifold.


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

  • [1] W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Progr. Math., vol. 61, Birkhäuser, Basel, 1985. MR 823981 (87h:53050)
  • [2] S. Chen and P. Eberlein, Isometry groups of simply connected manifolds of nonpositive curvature, Illinois J. Math. 24 (1980), 73-103. MR 550653 (82k:53052)
  • [3] P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-109. MR 0336648 (49:1421)
  • [4] F. Ohtsuka, On a relation between total curvature and Tits metric, Bull. Fac. Sci. Ibaraki Univ. Ser. A 20 (1988), 5-8. MR 951723 (89i:53031)
  • [5] -, On manifolds having some restricted ideal boundaries, Geom. Dedicata (to appear). MR 1104340 (92e:53059)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20, 53C23

Retrieve articles in all journals with MSC: 53C20, 53C23


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1074746-3
Keywords: Euclidean factor, Tits metric, polar point, Hadamard manifold
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society