Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.

it is easily seen that a motion and a homothetic transformation are both affine collineations and that an affine collineation preserves the curvature tensor. In [l ] one of the present authors proved that in a space of nonzero constant curvature a mapping preserving curvature is a motion. For an Einstein space with nonzero curvature scalar, a mapping preserving Ricci curvature is a motion; for ...

m *'* aiixr + ai2< + ■ ■ • + ai*+i°€li fi_, h, xk+i ak+nxi ~r an-i2a:2 + ■+ a*+i*+ia;i:+i where wi is zero or an integer less than n, is a collineation. As a result of Dr. Levi's article J it is possible to prove the converse proposition, namely, that every collineation in PG(k,pn) is of type (1). The following argument connects this theorem directly with our former article. It will be sufficie...

of order n on V . It follows that R induces a projective collineation φ on the (n−1)dimensional projective space PG(n−1, q). We call φ and any projective collineation conjugate to φ a Frobenius collineation. In the present paper we shall study the case n = 3, that is, the Frobenius collineations of the projective plane PG(2, q). Let P = PG(2, q). Then every Singer cycle σ (see Section 3) of P d...

We have shown in [2] that the full collineation group of any projective plane of order 12 is a (2, 3) group. It is of interest to determine the structure of this (2,3} group. As a first step in that direction, we have shown in [3] that a non-Abelian group of order 6 cannot act as a collineation group on any projective plane of order 12. As a second step, we have shown in [4] that there is no pr...

It is shown that a projective plane of odd order, with a collineation group acting primitively on the points of an invariant oval, must be desarguesian. Moreover, the group is actually doubly transitive, with only one exception. The main tool in the proof is that a collineation group leaving invariant an oval in a projective plane of odd order has 2-rank at most three.

Scene geometry can be inferred from point correspondences between two images. The inference process includes the selection of a model. Four models are considered: background (or null), collineation, affine fundamental matrix and fundamental matrix. It is shown how Minimum Description Length (MDL) can be used to compare the different models. The main result is that there is little reason for pre...

Scene geometry can be inferred from point correspondences between two images. The inference process includes the selection of a model. Four models are considered: background (or null), collineation, affine fundamental matrix and fundamental matrix. It is shown how Minimum Description Length (MDL) can be used to compare the different models. The main result is that there is little reason for pre...