Projective invariant metrics and open convex regular cones. I

Podestà, Fabio

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 81 (1987) no. 2, pp. 125-137

Résumé

In this work we give a characterization of the projective invariant pseudometric $P$, introduced by H. Wu, for a particular class of real $\mathbf{C}^{\infty}$-manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance $p$ of $P$ in open convex regular cones of $\mathbb{R}^{n}$, endowed with the characteristic metric.