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On quadrics poristically related to a rational norm curve

Published online by Cambridge University Press:  24 October 2008

B. Ramamurti
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Extract

The main object of this paper is to study the quadrics which have simultaneously certain poristic relations with a rational norm curve. We shall begin with a résumé of the work done in this direction in the ordinary space [3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 4 , October 1934 , pp. 381 - 388
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Meyer, , Apolarität und rationale Curven, p. 279.Google Scholar

† Vaidyanathaswamy, , Proc. Camb. Phil. Soc. 26 (1930), 206–219.CrossRefGoogle Scholar

‡ White, F. P., Proc. Camb. Phil. Soc. 23 (1927), 889CrossRefGoogle Scholar; also Vaidyanathaswamy, , Journ. London Math. Soc. 7 (1932), 52–57.CrossRefGoogle Scholar

§ Vaidyanathaswamy, , Journ. Indian Math. Soc. 18 (1929), 168–176.Google Scholar

* F. P. White, loc. cit.; see also Ramamurti, , Journ. London Math. Soc. 9 (1934), 102–104.CrossRefGoogle Scholar

* Vaidyanathaswamy, , Journ. London Math. Soc. 7 (1932), 52–57.CrossRefGoogle Scholar

† Vaidyanathaswamy and Ramamurti, “On the rational norm curve, III”, communicated for publication to the London Math. Soc.

* F. P. White, loc. cit.

† Though it is not defined as an envelope, the degenerate remarkable quadric locus shares with the inpolar quadric the property of having ∞1 inscribed simplexes of R n, self-polar with respect to it, since the correspondence determined by it is also closed. In this case, however, the simplexes have as a common element a [n − r], where r is the rank of the quadric locus.

* A [r − 1] is said to be chordal to a given curve when it cuts the curve in r points, and is said to be axial to the curve when it lies in n − r + 1 osculating primes of the curve.

† Ramamurti, loc. cit.

* For the contents of this paragraph, it will be helpful to refer to Wälsch, , Monatshefte für Mathematik und Physik, 6 (1895), §§ 1–5.Google Scholar