We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.
@article{bwmeta1.element.doi-10_2478_s11533-012-0082-y,
author = {Rui Albuquerque},
title = {On the characteristic connection of gwistor space},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {149-160},
zbl = {1273.53018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0082-y}
}
Rui Albuquerque. On the characteristic connection of gwistor space. Open Mathematics, Tome 11 (2013) pp. 149-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0082-y/
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