A unified approach to some theorems on homogeneous Riemannian and affine spaces
Homogeneous geodesics in a three-dimensional Lie group
O. Kowalski and J. Szenthe [KS] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic, i.eȯne 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 be a homogeneous Riemannian manifold where is the largest connected group of isometries and . Does always admit more than one homogeneous geodesic? (2) Suppose that admits linearly independent...
Three-dimensional curvature homogeneous hypersurfaces
This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers.
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