Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 3, page 207-210
  • ISSN: 1120-6330

Abstract

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We study local equivalence of left-invariant metrics with the same curvature on Lie groups G and G ¯ of dimension three, when G is unimodular and G ¯ is non-unimodular.

How to cite

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Lastaria, Federico G.. "Comparison of metrics on three-dimensional Lie groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.3 (1991): 207-210. <http://eudml.org/doc/244152>.

@article{Lastaria1991,
abstract = {We study local equivalence of left-invariant metrics with the same curvature on Lie groups \( G \) and \( \bar\{G\} \) of dimension three, when \( G \) is unimodular and \( \bar\{G\} \) is non-unimodular.},
author = {Lastaria, Federico G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Invariant metric; Invariant isometry; Singer invariant; left-invariant metrics},
language = {eng},
month = {9},
number = {3},
pages = {207-210},
publisher = {Accademia Nazionale dei Lincei},
title = {Comparison of metrics on three-dimensional Lie groups},
url = {http://eudml.org/doc/244152},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Lastaria, Federico G.
TI - Comparison of metrics on three-dimensional Lie groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/9//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 3
SP - 207
EP - 210
AB - We study local equivalence of left-invariant metrics with the same curvature on Lie groups \( G \) and \( \bar{G} \) of dimension three, when \( G \) is unimodular and \( \bar{G} \) is non-unimodular.
LA - eng
KW - Invariant metric; Invariant isometry; Singer invariant; left-invariant metrics
UR - http://eudml.org/doc/244152
ER -

References

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  1. BESSE, A. L., Einstein Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer Verlag, 1987. Zbl0613.53001MR867684
  2. LASTARIA, F. G., Homogeneous metrics with the same curvature. Simon Stevin Math J., to appear. Zbl0762.53034MR1162498
  3. LASTARIA, F. G., Metriche omogenee con la stessa curvatura. Tesi di dottorato di ricerca, Università di Milano. 
  4. MILNOR, J., Curvatures of left-invariant metrics on Lie groups. Adv. in Math., 21, 1976, 293-329. Zbl0341.53030MR425012
  5. NICOLODI, L. - TRICERRI, F., On two theorems of I. M. Singer about homogeneous spaces. Ann. of Global Anal. and Geom., to appear. Zbl0676.53058MR1088511DOI10.1007/BF00128003
  6. SINGER, I. M., Infinitesimally homogeneous spaces. Comm. Pure Appl. Math., 13, 1960, 685-697. Zbl0171.42503MR131248

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