Standard

On homogeneous geodesics and weakly symmetric spaces. / Berestovskiĭ, Valeriĭ Nikolaevich; Nikonorov, Yuriĭ Gennadievich.

в: Annals of Global Analysis and Geometry, Том 55, № 3, 01.04.2019, стр. 575-589.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Berestovskiĭ, VN & Nikonorov, YG 2019, 'On homogeneous geodesics and weakly symmetric spaces', Annals of Global Analysis and Geometry, Том. 55, № 3, стр. 575-589. https://doi.org/10.1007/s10455-018-9641-1

APA

Berestovskiĭ, V. N., & Nikonorov, Y. G. (2019). On homogeneous geodesics and weakly symmetric spaces. Annals of Global Analysis and Geometry, 55(3), 575-589. https://doi.org/10.1007/s10455-018-9641-1

Vancouver

Berestovskiĭ VN, Nikonorov YG. On homogeneous geodesics and weakly symmetric spaces. Annals of Global Analysis and Geometry. 2019 апр. 1;55(3):575-589. doi: 10.1007/s10455-018-9641-1

Author

Berestovskiĭ, Valeriĭ Nikolaevich ; Nikonorov, Yuriĭ Gennadievich. / On homogeneous geodesics and weakly symmetric spaces. в: Annals of Global Analysis and Geometry. 2019 ; Том 55, № 3. стр. 575-589.

BibTeX

@article{34d55bdd91254c04933247798e9bfd3e,
title = "On homogeneous geodesics and weakly symmetric spaces",
abstract = "In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an 1-parameter isometry group. As an application of this result, we provide a new proof of the fact that every weakly symmetric space is a geodesic orbit manifold, i.e. all its geodesics are homogeneous. We also study general properties of homogeneous geodesics, in particular, the structure of the closure of a given homogeneous geodesic. We present several examples where this closure is a torus of dimension ≥ 2 which is (respectively, is not) totally geodesic in the ambient manifold. Finally, we discuss homogeneous geodesics in Lie groups supplied with left-invariant Riemannian metrics.",
keywords = "Geodesic orbit Riemannian space, Homogeneous Riemannian manifold, Homogeneous space, Quadratic mapping, Totally geodesic torus, Weakly symmetric space",
author = "Berestovskiĭ, {Valeriĭ Nikolaevich} and Nikonorov, {Yuriĭ Gennadievich}",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature B.V.",
year = "2019",
month = apr,
day = "1",
doi = "10.1007/s10455-018-9641-1",
language = "English",
volume = "55",
pages = "575--589",
journal = "Annals of Global Analysis and Geometry",
issn = "0232-704X",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - On homogeneous geodesics and weakly symmetric spaces

AU - Berestovskiĭ, Valeriĭ Nikolaevich

AU - Nikonorov, Yuriĭ Gennadievich

N1 - Publisher Copyright: © 2018, Springer Nature B.V.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an 1-parameter isometry group. As an application of this result, we provide a new proof of the fact that every weakly symmetric space is a geodesic orbit manifold, i.e. all its geodesics are homogeneous. We also study general properties of homogeneous geodesics, in particular, the structure of the closure of a given homogeneous geodesic. We present several examples where this closure is a torus of dimension ≥ 2 which is (respectively, is not) totally geodesic in the ambient manifold. Finally, we discuss homogeneous geodesics in Lie groups supplied with left-invariant Riemannian metrics.

AB - In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an 1-parameter isometry group. As an application of this result, we provide a new proof of the fact that every weakly symmetric space is a geodesic orbit manifold, i.e. all its geodesics are homogeneous. We also study general properties of homogeneous geodesics, in particular, the structure of the closure of a given homogeneous geodesic. We present several examples where this closure is a torus of dimension ≥ 2 which is (respectively, is not) totally geodesic in the ambient manifold. Finally, we discuss homogeneous geodesics in Lie groups supplied with left-invariant Riemannian metrics.

KW - Geodesic orbit Riemannian space

KW - Homogeneous Riemannian manifold

KW - Homogeneous space

KW - Quadratic mapping

KW - Totally geodesic torus

KW - Weakly symmetric space

UR - http://www.scopus.com/inward/record.url?scp=85057869520&partnerID=8YFLogxK

U2 - 10.1007/s10455-018-9641-1

DO - 10.1007/s10455-018-9641-1

M3 - Article

AN - SCOPUS:85057869520

VL - 55

SP - 575

EP - 589

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

SN - 0232-704X

IS - 3

ER -

ID: 18186269