Holomorphic riemannian metrics in little dimension

Sorin Dumitrescu[1]

  • [1] Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1663-1690
  • ISSN: 0373-0956

Abstract

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We study holomorphic Riemannian metrics on compact complex threefolds. We show that, contrary to the situation in the real domain, a holomorphic Riemannian metric admits a "big" pseudogroup of local isometries. It follows that compact complex simply connected threefolds do not admit any holomorphic Riemannian metric.

How to cite

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Dumitrescu, Sorin. "Métriques riemanniennes holomorphes en petite dimension." Annales de l’institut Fourier 51.6 (2001): 1663-1690. <http://eudml.org/doc/115963>.

@article{Dumitrescu2001,
abstract = {Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension $3$. Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension $3$.},
affiliation = {Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay cedex (France)},
author = {Dumitrescu, Sorin},
journal = {Annales de l’institut Fourier},
keywords = {complex manifolds; holomorphic riemannian metrics; algebraic theory of invariants; pseudogroup of local isometries},
language = {fre},
number = {6},
pages = {1663-1690},
publisher = {Association des Annales de l'Institut Fourier},
title = {Métriques riemanniennes holomorphes en petite dimension},
url = {http://eudml.org/doc/115963},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Dumitrescu, Sorin
TI - Métriques riemanniennes holomorphes en petite dimension
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1663
EP - 1690
AB - Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension $3$. Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension $3$.
LA - fre
KW - complex manifolds; holomorphic riemannian metrics; algebraic theory of invariants; pseudogroup of local isometries
UR - http://eudml.org/doc/115963
ER -

References

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