Geodesic
C-Nodal Surfaces of Order Three
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 68-100

Voir la notice de l'article provenant de la source Cambridge University Press

The problem of describing a surface of order three can be said to originate in the mid-nineteenth century when A. Cayley discovered that a non-ruled cubic (algebraic surface of order three) may contain up to twenty-seven lines. Besides a classification of cubics, not much progress was made on the problem until A. Marchaud introduced his theory of synthetic surfaces of order three in [9]. While his theory resulted in a partial classification of a now larger class of surfaces, it was too general to permit a global description. In [1], we added a differentiability condition to Marchaud's definition. This resulted in a partial classification and description of surfaces of order three with exactly one singular point in [2]-[5]. In the present paper, we examine C-nodal surfaces and thus complete this survey. 
Bisztriczky, Tibor. C-Nodal Surfaces of Order Three. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 68-100. doi: 10.4153/CJM-1983-006-9
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[1] 1. Bisztriczky, T., Surfaces of order three with a peak. I, J. of Geometry 11 (1978), 55–83. Google Scholar

[2] 2. Bisztriczky, T., Surfaces of order three with a peak. II, J. of Geometry 11 (1978), 110–138. Google Scholar

[3] 3. Bisztriczky, T., Uniplanar surfaces of order three, Geometriae Dedicata 8 (1979), 259–277. Google Scholar

[4] 4. Bisztriczky, T., Biplanar surfaces of order three, Can. J. Math. 31 (1979), 396–418. Google Scholar

[5] 5. Bisztriczky, T., Biplanar surfaces of order three. II, Can. J. Math. 32 (1980), 839–866. Google Scholar

[6] 6. Bisztriczky, T., On surfaces of order three, Can. Math. Bull. 22 (1979), 351–355. Google Scholar

[7] 7. Bisztriczky, T., On the lines of a surface of order three, Math. Ann. 243 (1979), 191–195. Google Scholar

[8] 8. Haupt, O. and Kiinneth, H., Geometrische Ordnungen (Springer, Berlin, Heidelberg, New York, 1967). Google Scholar

[9] 9. Marchaud, A., Sur les surfaces du troisième ordre delà géométrie finie, J. Math. Pure Appi. 18 (1939), 323–362. Google Scholar

[10] 10. Marchaud, A., Sur les propriétés différentielles du premier ordre des surfaces simples de Jordan et quelques applications, Ann. Ec. Norm. Sup. 63 (1947), 81–108. Google Scholar

[11] 11. Marchaud, A., Sur les courbes et surfaces du troisième ordre en géométrie finie, Bull. Cl. Sci. Acad. Roy. Belgique 49 (1963), 555–575. Google Scholar

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