Projective invariant metrics and open convex regular cones. II

Fabio Podestà

Displaying similar documents to “Projective invariant metrics and open convex regular cones. II”

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

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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 $\mathbb{R}^{n}$ 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 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

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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.

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

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Families of Measurable Conic Sections in the Projective Space PR

Gioia Failla, Giovanni Molica Bisci (2007)

Bollettino dell'Unione Matematica Italiana

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In this note we prove the measurability of the family of non-degenerate conic sections in the projective space $P^{4}$ , obtained by cutting a non-degenerate quadratic cone by a linear variety of dimension two not containing the cone vertex.

Global minimal models for endomorphisms of projective space

Clayton Petsche, Brian Stout (2014)

Journal de Théorie des Nombres de Bordeaux

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We prove the existence of global minimal models for endomorphisms $φ : ℙ^{N} \to ℙ^{N}$ of projective space defined over the field of fractions of a principal ideal domain.

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

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A note on the countable extensions of separable $p^{ω + n}$ -projective abelian $p$ -groups

Peter Vassilev Danchev (2006)

Archivum Mathematicum

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It is proved that if $G$ is a pure $p^{ω + n}$ -projective subgroup of the separable abelian $p$ -group $A$ for $n \in N \cup {0}$ such that $| A / G | \leq ℵ_{0}$ , then $A$ is $p^{ω + n}$ -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

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Polynomial functions on the classical projective spaces

Yu. I. Lyubich, O. A. Shatalova (2005)

Studia Mathematica

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The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions ${| ⟨ x, \cdot ⟩ |}^{d}$ .

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

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The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{k ̅}^{m}$ , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{ℂ}^{m} .$

$v$ -projective symmetries of fibered manifolds

Cătălin Tigăeru (1998)

Archivum Mathematicum

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We prove that the set of the $v$ -projective symmetries is a Lie algebra.

Quadro-quadric Cremona transformations in low dimensions via the $J C$ -correspondence

Luc Pirio, Francesco Russo (2014)

Annales de l’institut Fourier

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It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra. We call this result the “”. In this article, we apply it to the study of quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension 4 and 5.