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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 ℝ 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 ℝ 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 relatedness and conformal flatness

Graham Hall (2012)

Open Mathematics

This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening...

Projectively flat Finsler metrics with orthogonal invariance

Libing Huang, Xiaohuan Mo (2013)

Annales Polonici Mathematici

We study Finsler metrics with orthogonal invariance. By determining an expression of these Finsler metrics we find a PDE equivalent to these metrics being locally projectively flat. After investigating this PDE we manufacture projectively flat Finsler metrics with orthogonal invariance in terms of error functions.

Propriétés projectives des espaces symétriques affines

Yvan Kerbrat (1980)

Annales de l'institut Fourier

On donne une description algébrique de l’ensemble des classes d’isomorphisme d’espaces symétriques affines connexes, simplement connexes et projectivement plats. On en déduit une classification des espaces symétriques affines connexes et projectivement plats et on détermine tous les espaces symétriques affines connexes admettant une transformation projective non affine.

Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures

S. Hronek, R. Suchánek (2022)

Archivum Mathematicum

We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional T * M . We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding equation. We also focus on pullbacks of the pseudo-metrics on two dimensional M , and describe the corresponding Hessian structures.

Pseudo-symmetric contact 3-manifolds III

Jong Taek Cho, Jun-ichi Inoguchi, Ji-Eun Lee (2009)

Colloquium Mathematicae

A trans-Sasakian 3-manifold is pseudo-symmetric if and only if it is η-Einstein. In particular, a quasi-Sasakian 3-manifold is pseudo-symmetric if and only if it is a coKähler manifold or a homothetic Sasakian manifold. Some examples of non-Sasakian pseudo-symmetric contact 3-manifolds are exhibited.

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