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Vol 5 No 2-3
Pages:
195-197
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RUS
Research article
Articles

IV order ruled surface with high symmetry and a curve with four cusp points

Authors:
E. S. Fedorov
Date submitted:
1914-06-01
Date accepted:
1914-08-24
Date published:
1914-12-01

Abstract

As is known, these fourth-order surfaces can be reproduced by two projective quadratic prima planes. The theory of these surfaces is presented in detailed manuals. In the general case, there is a hexaprima of points on the surface at which two rays of the surface intersect. Planes passing through such a pair of rays can be considered tangent planes, and since a flat section of a surface in the general case is a curve of order IV, it is clear that if a plane passes through one of the rays of the surface, then this curve splits into this ray and a curve of III order, and if the plane passes through a pair of rays, then the same curve breaks up into this pair and another conoprima; from here we see that the tangent planes passing through pairs of rays of the surface intersect this surface while still in conoprima.

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References

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