There are three kinds of Benz planes: Möbius planes, Laguerre planes and Minkowski planes. A Minkowski plane satisfying an additional axiom is connected with some other structure called a nearaffine plane. We construct an analogous structure for a Laguerre plane. Moreover, our description is common for both cases.
The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism to be a special Lagrangian linear subspace in . This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian is defined.
We give some examples of André-structures admitting translation groups which are transitive on the set of points but which are not normal in the dilatation group. André structures with this property seem to be new in the literature.
In questa Nota diamo una caratterizzazione dell'insieme di tutti i flocks lineari della quadrica iperbolica assolutamente irriducibile in .
In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness...