Generalised Surfaces in ℝ³

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, UK

ORCID

0000-0002-7437-5046

Document Type

Article

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Mathematical Proceedings of the Royal Irish Academy, vol. 104A, no. 2. © Royal Irish Academy

Abstract

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.

Recommended Citation

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.