Handbook of Pseudo-Riemannian Geometry and Supersymmetry


Full-Text PDF (229 KB) | Book articles | Book details

pp: 477–496

DOI: 10.4171/079-1/14

Twistor and reflector spaces of almost para-quaternionic manifolds

Stefan Ivanov[1], Ivan Minchev[2] and Simeon Zamkovoy[3]

(1) University of Sofia, Bulgaria
(2) University of Sofia, Bulgaria
(3) University of Sofia, Bulgaria

We investigate the integrability of 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 an arbitrary para-quaternionic connection. We show that if there exists an integrable structure then it is independent on the para-quaternionic connection. In dimension four, we express the ant-self-duality condition in terms of the Riemannian Ricci forms with respect to the associated para-quaternionic structure.

No keywords available for this article.

BACK TO TOP