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Projective invariant metrics and open convex regular cones. I

Fabio Podestà — 1987

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -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 n , endowed with the characteristic metric.

Projective invariant metrics and open convex regular cones. II

Fabio Podestà — 1987

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The aim of this work, which continues Part I with the same title, is to study a class of projective transformations of open, convex, regular cones in n and to prove a structure theorem for affine transformations of a restricted class of cones; we conclude with a version of the Schwarz Lemma holding for affine transformations.

Projective invariant metrics and open convex regular cones. II

Fabio Podestà — 1987

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

The aim of this work, which continues Part I with the same title, is to study a class of projective transformations of open, convex, regular cones in n and to prove a structure theorem for affine transformations of a restricted class of cones; we conclude with a version of the Schwarz Lemma holding for affine transformations.

Projective invariant metrics and open convex regular cones. I

Fabio Podestà — 1987

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -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 n , endowed with the characteristic metric.

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