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Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds

Stefan Ivanov·Ivan Minchev·Simeon Zamkovoy
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Abstract

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.

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Stefan Ivanov, Ivan Minchev, Simeon Zamkovoy. 2005-11-27. Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds. https://arxiv.org/abs/math/0511657

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