On δ-homogeneous Riemannian manifolds

Berestovskiî, V. N.; Nikonorov, Yu. G.

doi:10.1134/s1064562407040291

Cited by 28 publications

(107 citation statements)

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“…Note that generalized normal homogeneous Riemannian manifolds (δ-homogeneous manifold, in another terminology) constitute another important subclass of geodesic orbit manifold. All metrics from this subclass are of non-negative sectional curvature and have some other interesting properties (see details in [4][5][6]). In the paper [9], a classification of generalized normal homogeneous metrics on spheres and projective spaces is obtained.…”

Section: On Geodesic Orbit Manifoldsmentioning

confidence: 99%

“…1), and Sp(1) is the first factor in the group Sp(1) × Sp(n) ⊂ Sp(n + 1). The Lie algebra of the group Sp(n) • U (1) is l ⊕ sp(n) ⊂ sp(n + 1) in the decomposition (5). It is known that the homogeneous space Sp(n + 1)/Sp(n) • U (1) is diffeomorphic to CP 2n+1 , hence we get a representation of an odd-dimensional complex projective space.…”

Section: On Invariant Metrics and Transitive Actions Of Groupsmentioning

confidence: 99%

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Геодезически Орбитальные Метрики На Сферах

Nikonorov¹

2013

Владикавказский Математический Журнал

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Section: On Geodesic Orbit Manifoldsmentioning

confidence: 99%

Section: On Invariant Metrics and Transitive Actions Of Groupsmentioning

confidence: 99%

Геодезически Орбитальные Метрики На Сферах

Nikonorov¹

2013

Владикавказский Математический Журнал

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“…These spaces have interesting geometrical properties, but we will not persue here. We refer to the paper [13] by V. Berestovski ǐ and Yu.G. Nikonorov for more information in this direction.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous manifolds whose geodesics are orbits. Recent results and some open problems

Arvanitoyeorgos¹

2017

Irish Math. Soc. Bull.

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A homogeneous Riemannian manifold (M = G/K, g) is called a space with homogeneous geodesics or a G-g.o. space if every geodesic γ(t) of M is an orbit of a one-parameter subgroup of G, that is γ(t) = exp(tX) • o, for some non zero vector X in the Lie algebra of G. We give an exposition on the subject, by presenting techniques that have been used so far and a wide selection of previous and recent results. We discuss generalization to two-step homogeneous geodesics. We also present some open problems.

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“…The notion of δ-homogeneity was initially introduced for metric spaces in [6], while Riemannian δ-homogeneous manifolds were extensively studied in [2] (δ-homogeneous manifolds are also known as generalized normal homogeneous manifolds; see for example [4]). In [6] it is proved that every locally compact δ-homogeneous space of Alexandrov curvature bounded below has non-negative curvature (see also [14], [8] for Alexandrov spaces).…”

mentioning

confidence: 99%

“…In [2] it is proved that any δ-homogeneous manifold is geodesic orbit. The original proof relies on a series of results related to Killing vector fields on δ-homogeneous manifolds as well as on a topological characterization of δ-homogeneous manifolds.…”

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confidence: 99%