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Symmetric models of the real projective plane

Symmetric models of the real projective plane
Symmetric models of the real projective plane
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.
195-202
Farran, H.R.
eaa3d681-9d35-4e43-b7da-15d6512f5a60
Pinto, Maria do Rosario
0a7e9be9-0957-4173-8b73-e460dcffdfe9
Robertson, S.A.
95eb6b84-69cb-407a-8e43-12a12534cfdc
Farran, H.R.
eaa3d681-9d35-4e43-b7da-15d6512f5a60
Pinto, Maria do Rosario
0a7e9be9-0957-4173-8b73-e460dcffdfe9
Robertson, S.A.
95eb6b84-69cb-407a-8e43-12a12534cfdc

Farran, H.R., Pinto, Maria do Rosario and Robertson, S.A. (1999) Symmetric models of the real projective plane. Beiträge zur Algebra und Geometrie, 40 (1), 195-202.

Record type: Article

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.

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Published date: 1999

Identifiers

Local EPrints ID: 29907
URI: http://eprints.soton.ac.uk/id/eprint/29907
PURE UUID: 9388d025-32ef-4132-8957-f5c0bec9f77a

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Date deposited: 19 Mar 2007
Last modified: 22 Jul 2020 16:51

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