Let (M, g) be a spacetime, where M is a smooth, connected, Hausdorff four-dimensional manifold and g is smooth Lorentzian metric of signature (+ -) defined on M . The manifold M and the metric g are assumed smooth (C). A smooth vector field ξ is said to preserve a matter symmetry [1] on M if, for each smooth local diffeomorphism φt associated with ξ, the tensors T and φ∗tT are equal on the doma...

Let be Cayley’s ruled cubic surface in a projective three-space over any commutative field . We determine all collineations fixing , as a set, and all cubic forms defining . For both problems the cases turn out to be exceptional. On the other hand, if then the set of simple points of can be endowed with a non-symmetric distance function. We describe the corresponding circles, and we establish t...

We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentago...

We investigate collineation groups of a finite projective plane of odd order n fixing an oval and having two orbits on it, one of which is assumed to be primitive. The situation in which the group fixes a point off the oval is considered. We prove that it occurs in a Desarguesian plane if and only if (n + 1)/2 is an odd prime, the group lying in the normalizer of a Singer cycle of PGL(2, n) in ...