Metrics without isometries are generic

Pierre Mounoud (1)

1 IMB - Institut de Mathématiques de Bordeaux

We prove that for any compact manifold of dimension greater than $1$, the set of pseudo-Riemannian metrics having a trivial isometry group contains an open and dense subset of the space of metrics.

Domaines: Géométrie différentielle [math.DG]

Pierre Mounoud. Metrics without isometries are generic. Monatshefte für Mathematik, 2015, 176 (4), pp.603--606. ⟨10.1007/s00605-014-0614-6⟩. ⟨hal-00954353⟩