Results 151 to 160 of about 715 (188)

Parallel and totally geodesic hypersurfaces of non‐reductive homogeneous four‐manifolds

Mathematische Nachrichten, 2020
We classify totally geodesic and parallel hypersurfaces of four-dimensional nonreductive homogeneous pseudo-Riemannian ...
Giovanni Calvaruso, Reinier Storm, Joeri Van der Veken   +2 more
exaly   +2 more sources

Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

Geometriae Dedicata, 2021
Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric.
Andreas Arvanitoyeorgos, Nikolaos Panagiotis Souris, Arvanitoyeorgos Andreas   +2 more
exaly   +4 more sources

Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds

Journal of Geometry and Physics, 2021
Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M=G∕H,g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric.
Andreas Arvanitoyeorgos, Nikolaos Panagiotis Souris   +1 more
exaly   +2 more sources

Homogeneous geodesics in a three-dimensional Lie group. [PDF]

, 2002
\textit{O. Kowalski} and \textit{J. Szenthe} [Geom. Dedicata 81, 209--214 (2000; Zbl 0980.53061)] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic. Consequently, it was quite natural to ask whether there exist more homogeneous geodesics. \textit{O.\ Kowalski, S. Nikčević} and \textit{Z. Vlášek} in another paper
Marinosci, Rosa Anna
openaire   +3 more sources

Some of the next articles are maybe not open access.

Related searches:

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
openaire   +2 more sources

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
openaire   +1 more source

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
openaire   +2 more sources

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

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
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