Homogeneous geodesics in a three-dimensional Lie group

  title={Homogeneous geodesics in a three-dimensional Lie group},
  author={Rosa Anna Marinosci},
  • Rosa Anna Marinosci
  • Published 2010
O. Kowalski and J. Szenthe [KS] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic, i.e. one geodesic which is an orbit of a one-parameter group of isometries. In [KNV] the related two problems were studied and a negative answer was given to both ones: (1) Let M = K/H be a homogeneous Riemannian manifold where K is the largest connected group of isometries and dimM ≥ 3. Does M always admit more than one homogeneous geodesic? (2) Suppose that M = K/H… CONTINUE READING