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math.MG2012★ 1 cited
Affine polar spaces derived from polar spaces and Grassmann structures defined on them
K. Prażmowski, M. Żynel
We prove that an affine polar space in the meaning of Cohen and Shult can be recovered from one of the three adjacency relations on a Grassmann structure over it. The result direct…
math.MG2012
Affine polar spaces derived from symplectic spaces, their geometry and representations: alternating semiforms
K. Prażmowski, M. Żynel
Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a…
math.MG2012
Grassmannians of lines defined in the geometry of a pseudo-polarity
K. Prażmowski, M. Żynel
The regular point-line geometry with respect to a pseudo-polarity is introduced. It is weaker than the underlying metric-projective geometry. The automorphism group of this geometr…