caa a22 4500 475741188 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/BF02675348 doi (NATIONALLICENCE)springer-10.1007/BF02675348 Makhnev A. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, Ekaterinburg aut Affine ovoids and extensions of generalized quadrangles [Elektronische Daten] [A. Makhnev] A set Δ of vertices of a generalized quadrangle of order (s, t) is said to be a hyperoval if any line intersects Δ in either 0, or 2 points. A hyperoval Δ is called an affine ovoid if |Δ|=2st. It is well known that μ-subgraphs in triangular extensions of generalized quadrangles are hyperovals. In the present paper we prove that ifS is a triangular extension forGQ(s, t) with totally regular point graph Γ such that μ=2st, thens is even, Γ is an τ-antipodal graph of diameter 3 with τ=1+s/2, and eithers=2, ort=s+2. Kluwer Academic/Plenum Publishers, 2000 finite geometries nationallicence generalized quadrangles nationallicence nonoriented graphs nationallicence hyperovals nationallicence affine ovoids nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/2(2000-08-01), 232-236 0001-4346 68:2<232 2000 68 11006 https://doi.org/10.1007/BF02675348 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675348 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Makhnev A. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, Ekaterinburg aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/2(2000-08-01), 232-236 0001-4346 68:2<232 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer