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Some properties of the line of striction of a ruled surface

Published online by Cambridge University Press:  31 October 2008

Ram Behari
Ram Behari
Affiliation:
St Stephen's College, University of Delhi.
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1. It is known that

(i) the line of striction of a ruled surface is the locus of points at which the geodesic curvatures of the orthogonal trajectories of the generators vanish,

(ii) if at each point of a curve C on a surface, a tangent to the surface is drawn, and these tangents generate a ruled surface of which C is the line of striction, then, if each tangent is turned through a constant angle α about its point of contact in the tangent plane, the new set of tangents also form a ruled surface with C as a line of striction.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 31 , January 1939 , pp. xii - xiii
Copyright
Copyright © Edinburgh Mathematical Society 1939

References

1 See Forsyth, , “Differential Geometry,” p. 386.Google Scholar

2 See Richmond, , “A note upon some properties of the curve of striction,” Proceedings of the Edinburgh Math. Soc., 1923, p. 95Google Scholar, for a method of obtaining this result from geometrical considerations.

1 See Study, Geometrie der dynamen, p. 93Google Scholar; also Zindler, , Liniengeometrie, Vol. 31, p. 14.Google Scholar

2 Study, loc. cit., p. 303Google Scholar; Zindler, , loc. cit., p. 14.Google Scholar