  We present and analyze exact gyraton and nonexpanding gravitational wave
solutions of algebraic type II on backgrounds which are a direct-product of two
2-spaces of constant curvature, or more general type D spacetimes. This family
of electro-vacuum background spacetimes contains the Nariai, anti-Nariai and
Plebanski-Hacyan universes, conformally flat Bertotti-Robinson and Minkowski
spaces. The gyraton solutions are given in a simple Kundt metric form. They
belong to the recently discussed class of spacetimes with constant scalar
invariants (CSI) of the curvature tensor. We show that the Einstein equations
reduce to a set of linear equations on the transverse 2-space which can be
explicitly solved using the Green functions.
