Projective invariant metrics and open convex regular cones. I

Fabio Podestà

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1987)

  • Volume: 81, Issue: 2, page 125-137
  • ISSN: 1120-6330

Abstract

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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 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.

How to cite

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Podestà, Fabio. "Projective invariant metrics and open convex regular cones. I." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 81.2 (1987): 125-137. <http://eudml.org/doc/287186>.

@article{Podestà1987,
abstract = {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.},
author = {Podestà, Fabio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Projective connections; Regular cones; Projective transformations; symmetric complete connection; Ricci tensor; pseudometric; self-dual cones; Koecher norm},
language = {eng},
month = {6},
number = {2},
pages = {125-137},
publisher = {Accademia Nazionale dei Lincei},
title = {Projective invariant metrics and open convex regular cones. I},
url = {http://eudml.org/doc/287186},
volume = {81},
year = {1987},
}

TY - JOUR
AU - Podestà, Fabio
TI - Projective invariant metrics and open convex regular cones. I
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1987/6//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 2
SP - 125
EP - 137
AB - 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.
LA - eng
KW - Projective connections; Regular cones; Projective transformations; symmetric complete connection; Ricci tensor; pseudometric; self-dual cones; Koecher norm
UR - http://eudml.org/doc/287186
ER -

References

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  1. BORTOLOTTI, E. (1941) - Spazi a Connessione Proiettiva. Ed. Cremonese, Roma Zbl67.0676.01
  2. EISENHART, L.P. (1927) - Non-Riemannian Geometry, «Amer. Math. Soc. Colloquium», Publ., Vol. VIII. MR1466961JFM52.0721.02
  3. FRANZONI, T. and VESENTINI, E. (1980) - Holomorphic maps and invariant distances. North Holland, Amsterdam. Zbl0447.46040MR563329
  4. GENTILI, G. (1981) - Invariant Riemannian Geometry on Convex Cones. Tesi di Perfezionamento - Classe di Scienze - Scuola Normale Superiore, Pisa. 
  5. KOBAYASHI, S. (1984) - Projective Structures of hyperbolic type, Banach Centre Publications, vol. 12, Warsaw, 127-152. Zbl0558.53019MR961077
  6. KOBAYASHI, S. and SASAKI, (1979) - Projective Invariant Metrics for Einstein Space «Nagoya Math. Journal», 73, 171-174. Zbl0413.53030MR524014
  7. KOBAYASHI, S. and NOMIZU, K. (1963) - Foundations of Differential Geometry, vol. I, II, Interscience Publishers. Zbl0119.37502MR152974
  8. NAGANO, T. (1959) - The Projective Transformations on a Space with parallel Ricci Tensor, «Kodai Math. Sem. Reports», 11, 131-138. Zbl0097.37503MR109330
  9. RINOW, W. (1961) - Die innere Geometrie der metrischen Räurne, Springer Verlag, Berlin. Zbl0096.16302MR123969
  10. ROTHAUS, O. (1960) - Domains of Positivity. «Abh. Math. Sem.», 189, 189-225. Zbl0096.27903MR121810
  11. VINBERG, E.B. (1963) - Theory of Convex Homogeneous Cones, «Trans. Moscow Math. Soc.», 12, 340. Zbl0138.43301MR158414
  12. WU, H. (1981) - Some Theorems on projectively Hyperbolicity, «J. Math. Soc. Japan», 33, 79-104. Zbl0458.53016MR597482DOI10.2969/jmsj/03310079

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