Almost Product Structures Almost Quaternionic Structures of the Second Kind Product Twistor Space
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 28, No 2, (2002), 163p-174p
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.
∗Research supported in part by NSF grant INT-9903302.