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Generalised Surfaces In ℝ³, Brendan Guilfoyle, Wilhelm Klingenberg
Generalised Surfaces In ℝ³, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
The correspondence between 2-parameter families of oriented lines in ℝ³ and surfaces in Tℙ¹ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences generated by global sections of Tℙ¹ are investigated, and a number of theorems are proven that generalise results for closed convex surfaces in ℝ³.