In this paper we consider a harmonic Riemannian foliation ℱ, and study the transversal infinitesimal automorphisms of ℱ with certain additional properties like being transversal conformal or Killing (= metric). Such automorphisms (modulo Killing automorphisms) are related to the stability of ℱ. A special study is made for the case of a foliation with constant transversal scalar curvature, and more particularly with transversal Ricci curvature proportional to the transversal metric (Einstein foliation).
All Science Journal Classification (ASJC) codes
- Geometry and Topology