Mathematics | Physical Sciences and Mathematics
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.
Guilfoyle, B., & Klingenberg, W. (2004). GENERALISED SURFACES IN ℝ³. Mathematical Proceedings of the Royal Irish Academy 104(2), 199-209. doi:10.1353/mpr.2004.0013.