Propriétés projectives des espaces symétriques affines

Yvan Kerbrat

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 1, page 193-219
  • ISSN: 0373-0956

Abstract

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We give an algebraic description for the set of isomorphism classes of connected, simply connected, projectively flat, affine symmetric spaces. A classification of connected projectively flat affine symmetric spaces id deduced. Moreover, we determine all connected affine symmetric spaces admitting a non affine projective transformation.

How to cite

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Kerbrat, Yvan. "Propriétés projectives des espaces symétriques affines." Annales de l'institut Fourier 30.1 (1980): 193-219. <http://eudml.org/doc/74440>.

@article{Kerbrat1980,
abstract = {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.},
author = {Kerbrat, Yvan},
journal = {Annales de l'institut Fourier},
keywords = {affine symmetric spaces; projectively flat; projective transformation},
language = {fre},
number = {1},
pages = {193-219},
publisher = {Association des Annales de l'Institut Fourier},
title = {Propriétés projectives des espaces symétriques affines},
url = {http://eudml.org/doc/74440},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Kerbrat, Yvan
TI - Propriétés projectives des espaces symétriques affines
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 1
SP - 193
EP - 219
AB - 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.
LA - fre
KW - affine symmetric spaces; projectively flat; projective transformation
UR - http://eudml.org/doc/74440
ER -

References

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  1. [1]M. CAHEN, Y. KERBRAT, Transformations conformes des espaces symétriques pseudo-riemanniens, à paraître. Zbl0532.53037
  2. [2]S. ISHIHARA, Groups of projective transformations on a projectively connected manifold, Jap. J. Math., 25 (1955), 37-80. Zbl0074.17403MR18,599d
  3. [3]S. KOBAYASHI, Transformation groups in differential geometry, Springer-Verlag, 1972. Zbl0246.53031MR50 #8360
  4. [4]S. KOBAYASHI, K. NOMIZU, Foundations of differential geometry, vol. I, Interscience, 1963. Zbl0119.37502MR27 #2945
  5. [5]A. LICHNEROWICZ, Géométrie des groupes de transformations, Dunod, 1958. Zbl0096.16001MR23 #A1329
  6. [6]O. LOOS, Symmetric Spaces, vol. I, Benjamin, 1969. 
  7. [7]T. OCHIAI, Geometry associated with semi-simple flat homogeneous spaces, Trans. Amer. Math. Soc., 152 (1970), 159-193. Zbl0205.26004MR44 #2160
  8. [8]S. SCHOUTEN, Ricci-Calculus, Second edition, Springer-Verlag, 1954. Zbl0057.37803
  9. [9]J. WOLF, Spaces of constant curvature, Mc Graw-Hill, 1967. Zbl0162.53304MR36 #829

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