Results 121 to 130 of about 1,691 (159)

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.
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Homogeneous Geodesics in Homogeneous Affine Manifolds

Results in Mathematics, 2009
For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which involves the reductive decomposition \(\mathfrak{g} = \mathfrak{h} + \mathfrak{m}\) of the Lie algebra \(\mathfrak{g}\) of the isometry group G and the scalar product on \(\mathfrak{m}\) induced by ...
Zdeněk Dušek, Oldřich Kowalski, Zdeněk Vlášek   +2 more
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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
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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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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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Homogeneous Riemannian manifolds with only one homogeneous geodesic

Publicationes Mathematicae Debrecen, 2003
Summary: \textit{O. Kowalski} and \textit{J. Szenthe} [Geom. Dedicata 81, No. 1-3, 209--214 (2000; Zbl 0980.53061), Erratum ibid. 84, 331--332 (2001)] proved that each homogeneous Riemannian manifold \((M, g)\) admits at least one homogeneous geodesic, i.e., a geodesic which is an orbit of a one-parameter group of isometries.
Kowalski, Oldřich, Vlášek, Zdeněk
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Light-like homogeneous geodesics and the geodesic lemma for any signature

Publicationes Mathematicae Debrecen, 2007
Summary: Homogeneous geodesics on homogeneous Riemannian manifolds have been studied by many authors. The fundamental tool is the so-called geodesic lemma. On pseudo-Riemannian manifolds, a generalization of the geodesic lemma is necessary. Physicists already know and use the generalized version.
Dušek, Zdeněk, Kowalski, Oldřich
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