Killing Vector Fields of Generic Semi-Riemannian Metrics

Let M be a smooth oriented connected n-dimensional manifold and let \({\mathfrak{M}}\) be the space of pseudo-Riemannian metrics on M of a given signature \({(n^+, n^-), n^{+} + n^- = n > 1}\). A system of n metric invariants is attached to each metric in \({\mathfrak{M}}\), called the Ricci invariants, and by using the geometric properties of such invariants, the following result is proved: The subset \({\mathfrak{O} \subset \mathfrak{M}}\) of metrics with no Killing vector fields other than the trivial one is open and dense with respect to the strong topology.