Geodesic
Biplanar Surfaces of Order Three
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 396-418

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0. Introduction. A surface of order three, F, in the real projective threespace 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 the present paper, we classify and describe those biplanar F which contain the line τ 1 ∩ τ 2.We describe a surface by determining the tangent plane sections of the surface at the differentiable points. This approach was introduced in [1] and it is based upon A. Marchaud's definition of “surfaces of order three” in [4]. 
Bisztriczky, Tibor. Biplanar Surfaces of Order Three. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 396-418. doi: 10.4153/CJM-1979-044-3
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[1] 1. Bisztriczky, T., Surfaces of order three with a peak, I. J. of Geometry, 11/1 (1978), 55–83. Google Scholar

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[3] 3. Haupt, O. and Runneth, H., Geometrische ordnungen (Springer-Verlag, Berlin, 1967). Google Scholar

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