A canonical connection for Lie group actions (Q1895222)

An \(n\)-dimensional Riemannian manifold \(M\) is said to be of cohomogeneity one if it admits a Lie group of isometries with \((n - 1)\) as the maximal dimension of orbits. Extending to such manifolds the classical construction of the Ambrose-Singer connection of homogeneous Riemannian manifolds, the author gives necessary and sufficient conditions for \(M\) to be of cohomogeneity one.