Biplanar Surfaces of Order Three II

Bisztriczky, Tibor

Canadian journal of mathematics, Tome 32 (1980) no. 4, pp. 839-866

Résumé

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. F is biplanar if it contains exactly one non-differentiable point v and the set of tangents of F at v is the union of two distinct planes, say τ 1 and τ 2.In [2], we examined the biplanar surfaces containing the line τ 1 ⌒ τ 2. In the present paper, we classify and describe the biplanar F with the property that τ1 ⌒ τ 2⌒ F = {v}.We denote the planes, lines and points of P 3 by the letters α, β, ..., L, M, ... and p, q, ... respectively. For a collection of flats α, L, p, ..., 〈α, L, p, ...〉 denotes the flat of P 3 spanned by them. For a set M in P 3, denotes the flat of P 3 spanned by the points of .

Détail

DOI : 10.4153/CJM-1980-064-1

Bibliographie

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