Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T09:11:51.743Z Has data issue: false hasContentIssue false
  • English
  • Français

On quadrics poristically related to a rational norm curve

Published online by Cambridge University Press:  24 October 2008

B. Ramamurti
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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