Results 171 to 180 of about 639 (201)

Homogeneity and Curvatures of Geodesic Spheres

Monatshefte für Mathematik, 2006
The purpose of this paper is to link the study of geodesic spheres with the investigation of scalar curvature invariants. The whole space of scalar curvature invariants is generated by the so-called Weyl invariants. For an arbitrary simple Weyl invariant on a geodesic sphere, the authors give an explicit expression of the first terms in its power ...
Díaz-Ramos, J. Carlos, García-Río, Eduardo, Vanhecke, Lieven   +2 more
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Homogeneous geodesics in homogeneous Riemannian manifolds – examples

Geometry and Topology of Submanifolds X, 2000
In [8] the first author and J. Szenthe proved, for a general homogeneous Riemannian manifold, some existence theorems on geodesics which are orbits of one-parameter groups of isometries. The aim of the present paper is to provide examples showing that the results from [8] are optimal in some sense.
Kowalski, Oldrich, Nikcevic, Stana, Vlasek, Zdenek   +2 more
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On the Existence of Homogeneous Geodesics in Homogeneous Riemannian Manifolds

Geometriae Dedicata, 2000
Let \(M=G/H\), \(G\) a connected Lie group, \(H\subset G\) a closed subgroup, \(\varphi:G \times M\to M\) the canonical left action. If \(\nabla\) is an affine connection on \(M\) which is invariant by \(\varphi\) then a geodesic \(\gamma\) of \(\nabla\) is called homogeneous if it coincides with a 1-parameter subgroup, \(\gamma(t)=\varphi (\exp tx,z)\)
Kowalski, Oldřich, Szenthe, János
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Homogeneous geodesics and natural reductivity of homogeneous Gödel-type spacetimes

Journal of Geometry and Physics, 2021
Let \((M,g)\) be a homogeneous pseudo-Riemannian manifold and \(G\subset I_0(M,g)\) a connected Lie group of isometries acting transitively on \(M\), so that \((M,g)\) is identified with the pseudo-Riemannian homogeneous space \((G/H,g)\), where \(H\) is the isotropy group at some point \(P_0\in M=G/H\).
Calvaruso G., Zaeim A.
openaire   +1 more source

Manifolds With Homogeneous Geodesics

2020
This chapter is devoted to geodesic orbit Riemannian spaces and manifolds. Geodesic orbit Riemannian manifolds are characterized by the condition that every geodesic is an orbit of some 1-parameter isometry subgroup (geodesics with this property are called homogeneous).
Valerii Berestovskii, Yurii Nikonorov
openaire   +1 more source

Integrable geodesic flows on homogeneous spaces

Sbornik: Mathematics, 2001
Consider a compact Lie group \(G\) endowed with a bi-invariant metric, a closed subgroup \(H\), and the homogeneous space \(M= G/H\), endowed with its geodesic flow \(O\). Let \(f_1,\dots, f_\ell\) be a basis of \(O\)-invariant real functions on \(T^1M\). For \(x\in M\), consider the subspace \(F_x\) of \(T^*_x M\) spanned by \(df_1(x),\dots, df_\ell(x)
Bolsinov, A. V., Jovanovič, Božidar Žarko   +1 more
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Homogeneous geodesics in homogeneous Randers spaces -- examples

2020
Summary: In this paper, we study homogeneous geodesics in homogeneous Randers spaces. we give a four dimensional example and we obtain homogeneous geodesics of this space in some special cases.
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On the existence of homogeneous geodesic in homogeneous Finsler spaces

Journal of Geometry and Physics, 2018
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Zaili Yan, Libing Huang
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Geodesic graphs with homogeneity conditions

Doklady Mathematics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gavrilyuk, A. L., Makhnev, A. A.
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Magnetic Geodesic Flows on Homogeneous Manifolds

Russian Physics Journal, 2014
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openaire   +1 more source