Displaying similar documents to “Geodesic graphs on special 7-dimensional g.o. manifolds”

Homogeneous geodesics in a three-dimensional Lie group

Rosa Anna Marinosci (2002)

Commentationes Mathematicae Universitatis Carolinae

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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 M = K / H be a homogeneous Riemannian manifold where K is the largest connected group of isometries and dim M ≥ 3 . Does M always admit more than one homogeneous geodesic? (2) Suppose that M = K / H admits m = dim M linearly...

Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk

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A homogeneous Riemannian manifold M = G / H is called a “g.o. space” if every geodesic on M arises as an orbit of a one-parameter subgroup of G . Let M = G / H be such a “g.o. space”, and m an Ad ( H ) -invariant vector subspace of Lie ( G ) such that Lie ( G ) = m ⊕ Lie ( H ) . A is a map ξ : m → Lie ( H ) such that t ↦ exp ( t ( X + ξ ( X ) ) ) ( e H ) is a geodesic for every X ∈ m ∖ { 0 } . The author calculates explicitly such geodesic graphs for certain special 2-step nilpotent Lie groups. More precisely, he deals with “generalized Heisenberg groups” (also known as “H-type groups”) whose center has...