  The Gauss-Bonnet gravity is a special case of so-called Quadratic Gravity,
which is an extension of Einstein's theory with additional terms in action that
are quadratic combinations of the Riemann tensor and its contractions. These
corrections are needed, for example, in perturbative quantum gravity. We
consider the family of Kundt spacetimes, which is defined in a purely
geometrical way by admitting a shear-free, twist-free and expansion-free null
geodesic congruence. In particular, we focus on the Kundt solutions without
gyratonic terms, and we investigate the constraints imposed by the
Einstein-Gauss-Bonnet field equations. The conditions for the metrics to be of
various algebraic types are also studied.
