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On Surfaces of Order Three

Published online by Cambridge University Press:  20 November 2018

Tibor Bisztriczky
Tibor Bisztriczky*
Affiliation:
Department of Mathematics and Statistics, The University of Calgary Calgary, Alberta, T2N 1N4
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A surface of order three F in the real projective three-space P 3 is met by every line, not in F, in at most three points.

In the present paper, we determine the existence and examine the distribution of elliptic, parabolic and hyperbolic points; that is, the differentiable points of F which do not lie on any line contained in F.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 351 - 355
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Bisztriczky, T., Surfaces of order three with a peak. L, J. of Geometry, Vol. 22 (1) (1978), 55-83.Google Scholar
2. Haupt, O. and Künneth, H., Geometrische Ordnungen, Springer-Verlag, Berlin, 1967.Google Scholar
3. Marchaud, A., Sur les surfaces du troisième ordre de la Géométrie finie, J. Math. Pur. Appl. 18, (1939), 323-362.Google Scholar
4. Scherk, P., Über differenzierbare Kurven und Bögen. I. Zum Begriff der Charakteristik, Časopis Pěst. Mat. 66 (1937), 165-171.Google Scholar