Fundamental Types of Metric Affine Spaces

Henryk Oryszczyszyn

Warsaw University, Bialystok

Krzysztof Prazmowski

Warsaw University, Bialystok

Summary.

We distinguish in the class of metric affine spaces some fundamental types of them. First we can assume the underlying affine space to satisfy classical affine configurational axiom; thus we come to Pappian, Desarguesian, Moufangian, and translation spaces. Next we distinguish the spaces satisfying theorem on three perpendiculars and the homogeneous spaces; these properties directly refer to some axioms involving orthogonality. Some known relationships between the introduced classes of structures are established. We also show that the commonly investigated models of metric affine geometry constructed in a real linear space with the help of a symmetric bilinear form belong to all the classes introduced in the paper.

MML Identifier: EUCLMETR

Contents (PDF format)

Bibliography

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