Displaying similar documents to “On δ -homogeneous Riemannian manifolds. II.”

Four-dimensional curvature homogeneous spaces

Kouei Sekigawa, Hiroshi Suga, Lieven Vanhecke (1992)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.

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...

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 ( M = G / K , g ) is called homogeneous if it is an orbit of an one-parameter subgroup of G . In the case when M = G / H is a naturally reductive space, that is the G -invariant metric g is defined by some non degenerate biinvariant symmetric bilinear form B , all geodesics of M are homogeneous. We consider the case when M = G / K is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group G , and we give a simple necessary condition that M admits a non-naturally...