Generating Geodesic Flows and Supergravity Solutions

Understand

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories.

• The geodesics correspond to timelike respectively spacelike $p$-brane solutions when they are lifted over a $p$-dimensional flat space.
• In particular, we consider the problem of constructing \emph{the minimal generating solution}: A geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries.
• We give an intrinsic characterization of this solution in a wide class of orbits for various supergravities in different dimensions.