Degenerations of Miquel's Theorem in elation Laguerre planes

• Autores: Olaf Bröcker
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 67, Nº. 1-2, 2004, págs. 175-179
• Idioma: inglés
• DOI: 10.1007/s00010-003-2714-6
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• Resumen

  • For Laguerre planes we have several degenerations of Miquel's Theorem. From a recent result by N. Knarr we know that the eight point degeneration of Miquel's Theorem (M2) characterizes elation Laguerre planes. We prove that further degenerations with only four and six points hold in elation Laguerre planes. Thus, we have candidates characterizing elation Laguerre planes or a bigger class of Laguerre planes in a geometric way.