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A Property Characteristic of Quadrics of Revolution and General Cylinders
Published online by Cambridge University Press: 03 November 2016
Extract
The locus of the centres of spherical curvature of a singly infinite family of geodesics which pass through a regular point O on a surface S, one in each direction in the tangent plane there, is, in general, a twisted curve. It will be proved that the only real surfaces, at all points of which (excluding umbilics) this locus is a plane curve, are quadrics of revolution and general cylinders.
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- Research Article
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- Copyright © Mathematical Association 1946
References
page note 141 * Weatherburn, Differential Geometry, I, Art. 6.
page note 141 † Darboux, Théorie des Surfaces, Art. 510. When the curve is a geodesic, 
and the expression for “Laguerre’s function” gives the equivalent of (2) since
page note 142 * Darboux, Art. 513.
page note 142 † Blaschke, Vorsles. ü Differentialgeometrie, I, p. 142.
page note 143 * Blaschke, p. 140.