We investigate the integrability of natural almost complex structures on the
twistor space of an almost para-quaternionic manifold as well as the
integrability of natural almost paracomplex structures on the reflector space
of an almost para-quaternionic manifold constructed with the help of a
para-quaternionic connection. We show that if there is an integrable structure
it is independent on the para-quaternionic connection. In dimension four, we
express the anti-self-duality condition in terms of the Riemannian Ricci forms
with respect to the associated para-quaternionic structure.
Publié le : 2005-11-27
Classification:
Mathematics - Differential Geometry,
High Energy Physics - Theory,
Mathematical Physics,
53C15, 5350
@article{0511657,
author = {Ivanov, Stefan and Minchev, Ivan and Zamkovoy, Simeon},
title = {Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds},
journal = {arXiv},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/0511657}
}
Ivanov, Stefan; Minchev, Ivan; Zamkovoy, Simeon. Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511657/