On -homogeneous Riemannian manifolds. II.
Berestovskij, V.N., Nikonorov, Yu.G. (2009)
Sibirskij Matematicheskij Zhurnal
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Displaying similar documents to “Naturally reductive homogeneous spaces and generalized Heisenberg groups”
On -homogeneous Riemannian manifolds. II.
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 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...
Metrics with homogeneous geodesics on flag manifolds
Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)
Commentationes Mathematicae Universitatis Carolinae
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A geodesic of a homogeneous Riemannian manifold is called homogeneous if it is an orbit of an one-parameter subgroup of . In the case when is a naturally reductive space, that is the -invariant metric is defined by some non degenerate biinvariant symmetric bilinear form , all geodesics of are homogeneous. We consider the case when is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group , and we give a simple necessary condition that admits a non-naturally...
Geodesic graphs on special 7-dimensional g.o. manifolds
Zdeněk Dušek, Oldřich Kowalski (2006)
Archivum Mathematicum
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In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds and . They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining...