Symmetric models of the real projective plane
Farran, H.R., Pinto, Maria do Rosario and Robertson, S.A. (1999) Symmetric models of the real projective plane. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 40, (1), 195-202.
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Description/Abstract
We show that the symmetry group of a stable immersion of the real projective plane P in E^3 is either trivial or is cyclic of order 3, and that of a stable map of P in E^3 is conjugate to a subgroup of the full tetrahedral group. Thus Boy's surface, in its `standard' form, is the most symmetrical stable immersion of P in $E^3, and Steiner's surface is given by the most symmetrical stable map of P in E^3. We also construct a smooth embedding of P in E^4 with symmetry group SO(2) by orthogonal projection of the Veronese surface.
| Item Type: | Article |
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| Related URLs: | |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics |
| Item ID: | 29907 |
| Date Deposited: | 19 Mar 2007 |
| Last Modified: | 02 Mar 2012 12:27 |
| Contributors: | Farran, H.R. (Author) Pinto, Maria do Rosario (Author) Robertson, S.A. (Author) |
| Date: | 1999 |
| Status: | Published |
| Contact Email Address: | farran@math-1.sci.kuniv.edu.kw |
| URI: | http://eprints.soton.ac.uk/id/eprint/29907 |
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