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Completely regular ovals
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Antonio Maschietti
Published/Copyright:
August 10, 2006
Abstract
The following result concerning completely regular ovals is proved: Let Π be a projective plane of even order and let 𝒪 be a completely regular oval with nucleus N. Then Π 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.
Received: 2004-09-21
Published Online: 2006-08-10
Published in Print: 2006-07-01
© Walter de Gruyter
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Articles in the same Issue
- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
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- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
