Geodesic
Curves on Surfaces of Constant Width
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 15-22

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A surface S of constant width is the boundary of a convex set K of constant width in euclidean 3-dimensional space E3. (See [l] pp. 127–139. )Our first result concerns the interdependence of five properties which a curve on such a surface may possess. Let S be a surface of constant width D > 0 which satisfies the smoothness condition that it be a 2-dimensional submanifold of E3 of class C2. 
Armstrong, William W. Curves on Surfaces of Constant Width. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 15-22. doi: 10.4153/CMB-1966-002-2
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     author = {Armstrong, William W.},
     title = {Curves on {Surfaces} of {Constant} {Width}},
     journal = {Canadian mathematical bulletin},
     pages = {15--22},
     year = {1966},
     volume = {9},
     number = {1},
     doi = {10.4153/CMB-1966-002-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-002-2/}
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