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Isometric immersions into manifolds without conjugate points

Published online by Cambridge University Press:  24 October 2008

J. Bolton
J. Bolton
Affiliation:
University of Durham
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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

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References

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