Geodesic
A Product Twistor Space
Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 163-174.

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In previous work a hyperbolic twistor space over a paraquaternionic Kähler manifold was defined, the fibre being the hyperboloid model of the hyperbolic plane with constant curvature −1. Two almost complex structures were defined on this twistor space and their properties studied. In the present paper we consider a twistor space over a paraquaternionic Kähler manifold with fibre given by the hyperboloid of 1-sheet, the anti-de-Sitter plane with constant curvature −1. This twistor space admits two natural almost product structures, more precisely almost para-Hermitian structures, which form the objects of our study.
Keywords: Almost Product Structures, Almost Quaternionic Structures of the Second Kind, Product Twistor Space 
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Blair, David. A Product Twistor Space. Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 163-174. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_2_a4/