Compatible complex structures on twistor space

Guillaume Deschamps[1]

  • [1] Laboratoire de mathematiques de Brest UMR 6205 6 avenue de Gorgeu 29238 Brest cedex 3 France

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2219-2248
  • ISSN: 0373-0956

Abstract

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Let M be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space Z admits a natural metric. The aim of this article is to study properties of complex structures on Z which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on M (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space Z .

How to cite

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Deschamps, Guillaume. "Compatible complex structures on twistor space." Annales de l’institut Fourier 61.6 (2011): 2219-2248. <http://eudml.org/doc/219683>.

@article{Deschamps2011,
abstract = {Let $M$ be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space $Z$ admits a natural metric. The aim of this article is to study properties of complex structures on $ Z$ which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on $M$ (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space $Z$.},
affiliation = {Laboratoire de mathematiques de Brest UMR 6205 6 avenue de Gorgeu 29238 Brest cedex 3 France},
author = {Deschamps, Guillaume},
journal = {Annales de l’institut Fourier},
keywords = {twistor space; complex structure; scalar-flat; scalar-flat Kähler; locally conformally Kähler; quaternionic Kähler},
language = {eng},
number = {6},
pages = {2219-2248},
publisher = {Association des Annales de l’institut Fourier},
title = {Compatible complex structures on twistor space},
url = {http://eudml.org/doc/219683},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Deschamps, Guillaume
TI - Compatible complex structures on twistor space
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2219
EP - 2248
AB - Let $M$ be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space $Z$ admits a natural metric. The aim of this article is to study properties of complex structures on $ Z$ which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on $M$ (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space $Z$.
LA - eng
KW - twistor space; complex structure; scalar-flat; scalar-flat Kähler; locally conformally Kähler; quaternionic Kähler
UR - http://eudml.org/doc/219683
ER -

References

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