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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 P3 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.

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