In this paper, we investigate the evolution of curves of the projective plane according to a family of projective invariant intrinsic equations. This is motivated by previous work for the Euclidean 9, 10, 13] and the aane cases 19, 20, 3, 2] as well as by applications in the perception of two-dimensional shapes. We establish the evolution laws for the projective arclength and curvature. Among t...

The projective shape of a configuration consists of the information that is invariant under projective transformations. It encodes the information about an object reconstructable from uncalibrated camera views. The space of projective shapes of k points in RP is by definition the quotient space of k copies of RP modulo the action of the projective linear group PGLpdq. A detailed examination of ...

Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F -algebra automorphisms. We study the ideals and subalgebras of A which are preserved by the group action. Let V be the unique simple module of A. We show that V is a projective representation of G and A = EndD(V ) makes V into a projective representation. We then prove that there is a natu...

We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...