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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Polar spaces embedded in projective spaces

Gavin J. Seal

Citation Information: Advances in Geometry. Volume 5, Issue 3, Pages 353–361, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advg.2005.5.3.353, July 2005

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Let P be a polar space induced by a quasipolarity on a projective space G. In this article, we give sufficient conditions for an embedding (i.e. an incidence-preserving map which is injective on points and lines) of P into a projective space H to be extendable to an incidencepreserving map from G to H. As a consequence, we obtain conditions for such an embedding to be induced by a semilinear map between the overlying vector spaces.

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