Harmonic morphisms between Weyl spaces and twistorial maps II

Eric Loubeau[1]; Radu Pantilie[2]

  • [1] Université de Bretagne Occidentale Département de Mathématiques Laboratoire C.N.R.S. U.M.R. 6205 6, Avenue Victor Le Gorgeu, CS 93837 29238 Brest Cedex 3 (France)
  • [2] Institutul de Matematică “Simion Stoilow” al Academiei Române C.P. 1-764 014700, Bucureşti (România)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 2, page 433-453
  • ISSN: 0373-0956

Abstract

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We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being a harmonic morphism naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces of dimensions four and three. Also, we give a thorough description of the twistorial maps with one-dimensional fibres from four-dimensional Weyl spaces endowed with the almost twistorial structure of Eells and Salamon.

How to cite

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Loubeau, Eric, and Pantilie, Radu. "Harmonic morphisms between Weyl spaces and twistorial maps II." Annales de l’institut Fourier 60.2 (2010): 433-453. <http://eudml.org/doc/116277>.

@article{Loubeau2010,
abstract = {We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being a harmonic morphism naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces of dimensions four and three. Also, we give a thorough description of the twistorial maps with one-dimensional fibres from four-dimensional Weyl spaces endowed with the almost twistorial structure of Eells and Salamon.},
affiliation = {Université de Bretagne Occidentale Département de Mathématiques Laboratoire C.N.R.S. U.M.R. 6205 6, Avenue Victor Le Gorgeu, CS 93837 29238 Brest Cedex 3 (France); Institutul de Matematică “Simion Stoilow” al Academiei Române C.P. 1-764 014700, Bucureşti (România)},
author = {Loubeau, Eric, Pantilie, Radu},
journal = {Annales de l’institut Fourier},
keywords = {Harmonic morphism; Weyl space; twistorial map; harmonic morphism},
language = {eng},
number = {2},
pages = {433-453},
publisher = {Association des Annales de l’institut Fourier},
title = {Harmonic morphisms between Weyl spaces and twistorial maps II},
url = {http://eudml.org/doc/116277},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Loubeau, Eric
AU - Pantilie, Radu
TI - Harmonic morphisms between Weyl spaces and twistorial maps II
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 2
SP - 433
EP - 453
AB - We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being a harmonic morphism naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces of dimensions four and three. Also, we give a thorough description of the twistorial maps with one-dimensional fibres from four-dimensional Weyl spaces endowed with the almost twistorial structure of Eells and Salamon.
LA - eng
KW - Harmonic morphism; Weyl space; twistorial map; harmonic morphism
UR - http://eudml.org/doc/116277
ER -

References

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