Quarter-BPS solutions in three-dimensional N=16 supergravity and the Liouville equation

We show how, by assuming at least eight real timelike supersymmetries in the maximally supersymmetric three-dimensional ungauged supergravity and a further simplifying ansatz, we are naturally led to a pair of Liouville field equations. These are solvable in terms of two meromorphic functions, and we present a novel and interesting large class of quarter-supersymmetric backgrounds. We also show that there are no solutions that preserve only six or seven real timelike supersymmetries. The solution relies on the classification of complex spinors of Spin(8) to which the problem quickly reduces.