Compact Riemannian Manifolds with Homogeneous Geodesics
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Compact Riemannian Manifolds with Homogeneous Geodesics
|
|
| Creator |
Alekseevsky, D.V.
Nikonorov, Y.G. |
|
| Description |
A homogeneous Riemannian space (M = G/H,g) is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group G. We study the structure of compact GO-spaces and give some sufficient conditions for existence and non-existence of an invariant metric g with homogeneous geodesics on a homogeneous space of a compact Lie group G. We give a classification of compact simply connected GO-spaces (M = G/H,g) of positive Euler characteristic. If the group G is simple and the metric g does not come from a bi-invariant metric of G, then M is one of the flag manifolds M₁ = SO(2n+1)/U(n) or M₂ = Sp(n)/U(1)·Sp(n–1) and g is any invariant metric on M which depends on two real parameters. In both cases, there exists unique (up to a scaling) symmetric metric g₀ such that (M,g0) is the symmetric space M = SO(2n+2)/U(n+1) or, respectively, CP²n⁻¹. The manifolds M₁, M₂ are weakly symmetric spaces.
|
|
| Date |
2019-02-19T17:31:47Z
2019-02-19T17:31:47Z 2009 |
|
| Type |
Article
|
|
| Identifier |
Compact Riemannian Manifolds with Homogeneous Geodesics / D.V. Alekseevsky, Y.G. Nikonorov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 28 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 53C20; 53C25; 53C35 http://dspace.nbuv.gov.ua/handle/123456789/149121 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|