Conformally parallel Spin(7) structures on solvmanifolds

In this paper we review the Spin(7) geometry in relation to solvmanifolds. Starting from a 7 -dimensional nilpotent Lie group N endowed with an invariant G2 structure, we present an example of a homogeneous conformally parallel Spin(7) metric on an associated solvmanifold. It is thought that this paper could lead to very interesting and exciting areas of research and new results in the direction of (locally conformally) parallel Spin(7) structures.