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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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.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics
|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)
|Contact Email Address:||firstname.lastname@example.org|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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