A hyperbolic twistor space.
We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.
∗Research supported in part by NSF grant INT-9903302.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...
In this paper we study -recurrence -curvature tensor in-contact metric manifolds.
We classify the -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure we describe the space of symplectic forms which are compatible with .
Identities for the curvature tensor of the Levi-Cività connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established.