Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T09:05:59.890Z Has data issue: false hasContentIssue false
  • English
  • Français

Transnormal hypersurfaces

Published online by Cambridge University Press:  24 October 2008

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

Extract

Let M be a C∞ manifold smoothly embedded as a convex hypersurface of Euclidean n-space n. M has constant width if the distance between each pair of parallel supporting hyperplanes in n is equal. This is equivalent to the condition that any chord of M normal to M at one end-point be normal to M at both end-points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 43 - 48
Copyright
Copyright © Cambridge Philosophical Society 1973

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)Bishop, R. and Crittenden, R.Geometry of manifolds (Academic Press, New York, 1964).Google Scholar
(2)Reinhart, B.Foliated manifolds with bundle-like metrics. Ann. of Math. 69 (1959), 119–131.CrossRefGoogle Scholar
(3)Robertson, S. A.Generalised constant width for manifolds. Michigan Math. J. 11 (1964), 97–105.CrossRefGoogle Scholar
(4)Robertson, S. A.On transnormal manifolds. Topology 6 (1967), 117–123.CrossRefGoogle Scholar
(5)Rosenberg, H.Actions of ℝn on manifolds. Comment. Math. Helv. 41 (1966), 170–178.CrossRefGoogle Scholar
(6)Warner, F. W.Extension of the Rauch comparison theorem to submanifolds. Trans. Amer. Math. Soc. 122 (1966), 341–356.Google Scholar