Results 171 to 180 of about 912 (205)

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 ...
Zdenek Dusek, Oldrich Kowalski, Kowalski Oldrich   +2 more
exaly   +2 more sources

Homogeneous geodesics in homogeneous Riemannian manifolds – examples [PDF]

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   +2 more sources

Geodesics and Jacobi Fields in Bounded Homogeneous Domains

Proceedings of the American Mathematical Society, 1983
The authors study bounded homogeneous domains in \({\mathbb{C}}^ n\) endowed with the Bergman metric. In case D is symmetric it is well known that the sectional curvature is nonpositive, and as a consequence D has no focal points (in the sense that any nontrivial Jacobi field along a nontrivial geodesic \(\gamma\) vanishing at \(\gamma\) (0) has ...
D'Atri, J. E., Zhao, Yanda
openaire   +2 more sources

Two-step homogeneous geodesics in pseudo-Riemannian manifolds

Annals of Global Analysis and Geometry, 2021
Given a homogeneous pseudo-Riemannian space (G/H,⟨,⟩), a geodesic γ: I→ G/ H is said to be two-step homogeneous if it admits a parametrization t= φ(s) (s affine parameter) and vectors X, Y in the Lie algebra g, such that γ(t) = exp (tX) exp (tY) · o, for
Andreas Arvanitoyeorgos, Giovanni Calvaruso, Nikolaos Panagiotis Souris   +2 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

Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

Advances in Geometry, 2008
We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [2] and [5], this leads to the full classification of three-dimensional ...
G Calvaruso
exaly   +2 more sources

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 pseudo-Riemannian nilmanifolds [PDF]

Advances in Geometry, 2016
We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries.
Viviana Del Barco
exaly   +2 more sources

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

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