Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds

Ivanov, Stefan; Minchev, Ivan; Zamkovoy, Simeon

Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds

Authors

Ivanov, Stefan

Minchev, Ivan

Zamkovoy, Simeon

Description

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.
LaTeX, 16 pages, no figures