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B. Ramamurthi

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B. Ramamurthi , C. N. Srinivasiengar

Abstract

It is well known that the line of striction of a regulus on a quadric is a rational quartic of type (1,3) cutting every generator of the regulus at a single point and every generator of the other regulus in three points. The rational quartic curve R⁴ in [3] has been studied in detail from the projective point of view. In this paper, the metrical specialisations consequent to the metrical definition of the line of striction, and a few allied problems are considered.

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B. Ramamurthi ¹

Affiliations
1 Annamalai University, IN

Abstract

The rational curve Rⁿ(3) of order n in [3], whose tangents belong to a linear complex, has been studied in detail by several writers. Picard showed that such a curve possesses in general 2n-6 points of inflexion. G. H. Grace attempted to prove the converse, that if an Rⁿ(3) has 2n-6 inflexions its tangents belong to a linear complex. The proof was however faulty, and M. F. Egan gave an example of a sextic curve for which the converse theorem is not true.

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