Abelian simply transitive affine groups of symplectic type

Oliver Baues[1]; Vicente Cortés[2]

  • [1] ETH-Zürich, Departement Mathematik, Rämistrasse 101, Ch-8092 Zürich
  • [2] Université de Nancy I, Institut Élie Cartan, BP 239 54506 Vandoeuvre-les-Nancy Cedex (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 6, page 1729-1751
  • ISSN: 0373-0956

Abstract

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The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.

How to cite

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Baues, Oliver, and Cortés, Vicente. "Abelian simply transitive affine groups of symplectic type." Annales de l’institut Fourier 52.6 (2002): 1729-1751. <http://eudml.org/doc/116025>.

@article{Baues2002,
abstract = {The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.},
affiliation = {ETH-Zürich, Departement Mathematik, Rämistrasse 101, Ch-8092 Zürich; Université de Nancy I, Institut Élie Cartan, BP 239 54506 Vandoeuvre-les-Nancy Cedex (France)},
author = {Baues, Oliver, Cortés, Vicente},
journal = {Annales de l’institut Fourier},
keywords = {affine transformations; flat symplectic connections; special Kähler manifolds; affine groups of symplectic type; affine transformation; special Kaehler manifolds},
language = {eng},
number = {6},
pages = {1729-1751},
publisher = {Association des Annales de l'Institut Fourier},
title = {Abelian simply transitive affine groups of symplectic type},
url = {http://eudml.org/doc/116025},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Baues, Oliver
AU - Cortés, Vicente
TI - Abelian simply transitive affine groups of symplectic type
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 6
SP - 1729
EP - 1751
AB - The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.
LA - eng
KW - affine transformations; flat symplectic connections; special Kähler manifolds; affine groups of symplectic type; affine transformation; special Kaehler manifolds
UR - http://eudml.org/doc/116025
ER -

References

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  9. S. Kobayashi, Transformation groups in differential geometry, (1972), Springer-Verlag Zbl0246.53031MR355886
  10. Z. Lu, A note on special Kähler manifolds, Math. Ann 313 (1999), 711-713 Zbl1021.53046MR1686939
  11. K. Nomizu, T. Sasaki, Affine differential geometry. Geometry of affine immersions, 111 (1994), Cambridge University Press, Cambridge Zbl0834.53002MR1311248
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