On a class of geodesic orbit spaces with abelian isotropy subgroup

Souris, Nikolaos Panagiotis

doi:10.1007/s00229-020-01236-9

Cited by 9 publications

(10 citation statements)

References 30 publications

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“…For the necessity part, assume initially that n 1 = • • • = n s = 2 so that H is abelian. Since G is semisimple, the main results in [24] imply that any g.o. metric on G/H is normal, and hence Theorem 1.1 follows in this case.…”

Section: So(nmentioning

confidence: 99%

“…The classification of g.o. spaces remains an open problem, whereas several partial classifications have been obtained ( [2], [3], [12], [13], [14], [16], [24], [27] to name a few).…”

Section: Introductionmentioning

confidence: 99%

“…When G is compact semisimple, the classification of the g.o. spaces (G/H, g) with H abelian and H simple has been obtained in the works [24] and [14] respectively. On the other hand, the classification of compact g.o.…”

Section: Introductionmentioning

confidence: 99%

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Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

Arvanitoyeorgos¹,

Souris²,

Statha³

2021

Preprint

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Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M = G/H, g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric. We study the geodesic orbit spaces of the form (G/H, g), such that G is one of the compact classical Lie groups SO(n), U (n), and H is a diagonally embedded product H1 × • • • × Hs, where Hj is of the same type as G. This class includes spheres, Stiefel manifolds, Grassmann manifolds and real flag manifolds. The present work is a contribution to the study of g.o. spaces (G/H, g) with H semisimple.

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Section: So(nmentioning

confidence: 99%

“…The classification of g.o. spaces remains an open problem, whereas several partial classifications have been obtained ( [2], [3], [12], [13], [14], [16], [24], [27] to name a few).…”

Section: Introductionmentioning

confidence: 99%

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Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

Arvanitoyeorgos¹,

Souris²,

Statha³

2021

Preprint

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“…When G is compact semisimple, the classification of the g.o. spaces (G/H, g) with H abelian and H simple has been obtained in the works [20] and [11] respectively. On the other hand, the classification of compact g.o.…”

Section: Introductionmentioning

confidence: 99%

“…Then Equation(19) along with Lemma 4.2 yield0 = λ[a, e 12 ] + λ[a, X 12 ] + 2(λ − µ)f 21 . (20)By the ad(h)-invariance of m ij and the fact that a ∈ h, the first two terms of Equation(20) lie in m 01 and m 12 respectively, while the last term lies in m 01 . Therefore, Equation (20) yields the systemλ[a, e 12 ] + 2(λ − µ)f 21 = 0 (21) λ[a, X 12 ] = 0.…”

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confidence: 99%

Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds

Arvanitoyeorgos,

Souris,

Statha

2021

Preprint

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Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M = G/H, g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric. We study the geodesic orbit spaces of the form (Sp(nSuch spaces include spheres, quaternionic Stiefel manifolds, Grassmann manifolds and quaternionic flag manifolds. The present work is a contribution to the study of g.o. spaces (G/H, g) with H semisimple.

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Compact geodesic orbit spaces with a simple isotropy group

2022

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Let $$M=G/H$$ M = G / H be a compact, simply connected, Riemannian homogeneous space, where G is (almost) effective and H is a simple Lie group. In this paper, we first classify all G-naturally reductive metrics on M, and then all G-geodesic orbit metrics on M.

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On a class of geodesic orbit spaces with abelian isotropy subgroup

Cited by 9 publications

References 30 publications

Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds

Compact geodesic orbit spaces with a simple isotropy group

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