Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-04T17:44:35.004Z Has data issue: false hasContentIssue false
  • English
  • Français

Isometric immersions into manifolds without conjugate points

Published online by Cambridge University Press:  24 October 2008

J. Bolton
J. Bolton
Affiliation:
University of Durham
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction and statement of results. Let f: Mn-1 → ℝn be an immersion into Euclidean space ℝn. Each unit vector v to ℝn determines a height function bv: ℝn → ℝ. The corresponding half-space Lv = b-1([0, ∞) has boundary Hv = (b−1). and L is a (globally) supporting half-space for M at m є M if (m) є H and f(M) ∩ Lv = f(M) ∩ Hv.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 2 , September 1982 , pp. 243 - 250
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Alexander, S.Locally convex hypersurfaces of negatively curved spaces. Proc. Amer. Math. Soc. 64 (1977), 321–325.CrossRefGoogle Scholar
(2)Bolton, J.Conditions under which a geodesic flow is Anosov. Math. Ann. 240 (1979), 103–113.CrossRefGoogle Scholar
(3)Bolton, J.On Riemannian immersions without focal points. J. Land. Math. Soc. (To appear.)Google Scholar
(4)Docarmo, M. P. and Lima, E.Isometric immersions with semi-definite second quadratic forms. Arch. Math. (Basel) 20 (1969), 173–175.CrossRefGoogle Scholar
(5)Eschenburg, J.-H.Horospheres and the stable part of the geodesic flow. Math. Z. 153 (1977), 237–251.CrossRefGoogle Scholar
(6)Eschenburg, J.-H. and O'sullivan, J. J.Growth of Jacobi fields and divergence of geodesies. Math. Z. 150 (1976), 221–237.CrossRefGoogle Scholar
(7)Hicks, N. J.Notes on Differential Geometry (Van Nostrand Beinhold, New York, 1965).Google Scholar
(8)Kobayashi, S. and Nomizu, K.Foundations of differential geometry, vol. 1 (Wiley-Inter-science, New York, 1963).Google Scholar