  The asymmetric skew divergence smooths one of the distributions by mixing it,
to a degree determined by the parameter $\lambda$, with the other distribution.
Such divergence is an approximation of the KL divergence that does not require
the target distribution to be absolutely continuous with respect to the source
distribution. In this paper, an information geometric generalization of the
skew divergence called the $\alpha$-geodesical skew divergence is proposed, and
its properties are studied.
