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Antonio Maschietti

Completely regular ovals

Keywords: Projective plane, oval, spread, symplectic translation plane

The following result concerning completely regular ovals is proved: Let &Pgr; be a projective plane of even order and let 𝒪 be a completely regular oval with nucleus N. Then &Pgr; is (N,N)-transitive. Combining this result with previous results [A. Maschietti, Symplectic translation planes and line ovals. Adv. Geom. 3 (2003), 123–143. MR1967995 (2004c:51008) Zbl 1030.51002] one obtains: A projective plane of even order admits a completely regular oval if and only if the plane is dual to a symplectic translation plane.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 6, 07/2006
Pages: 361 - 377

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