Results 11 to 20 of about 912 (205)
On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spaces [PDF]
Bulletin of the Iranian Mathematical Society, 2019 Recently, it is shown that each regular homogeneous Finsler space $M$ admits at least one homogeneous geodesic through any point $o\in M$. The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous $(α,β)$-spaces, specially, homogeneous Kropina spaces.
M. Hosseini, Hamid Reza Salimi Moghaddam
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The affine approach to homogeneous geodesics in homogeneous Finsler spaces [PDF]
Archivum Mathematicum, 2018 In a recent paper, it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. For the proof, the algebraic method dealing with the reductive decomposition of the Lie algebra of the isometry group was used. However, the proof contains a serious gap.
Dušek, Zdeněk
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Homogeneous geodesics and g.o. manifolds
, 2018 One interesting problem in pseudo-Riemannian geometry is the description of geodesics. In order to obtain some simplifications to the problem, symmetry conditions on the manifold are assumed. In this framework, the problem of the description of geodesics in homogeneous pseudo-Riemannian manifolds \((M,g)\) is considered. Motivated by the facts that the
Zdeněk Dušek,
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Geodesically equivalent metrics on homogenous spaces [PDF]
Czechoslovak Mathematical Journal, 2018 Two metrics on a manifold are geodesically equivalent if sets of their unparameterized geodesics coincide. In this paper we show that if two left $G$-invariant metrics of arbitrary signature on homogenous space $G/H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection.
Bokan, Neda +2 more
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Homogeneous geodesics in sub-Riemannian geometry
, 2022 We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum.
Podobryaev, A. V.
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Riemannian M-spaces with homogeneous geodesics [PDF]
Annals of Global Analysis and Geometry, 2018 We investigate homogeneous geodesics in a class of homogeneous spaces called $M$-spaces, which are defined as follows. Let $G/K$ be a generalized flag manifold with $K=C(S)=S\times K_1$, where $S$ is a torus in a compact simple Lie group $G$ and $K_1$ is the semisimple part of $K$.
Arvanitoyeorgos, Andreas +2 more
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Geodesic deviation equation in generalized hybrid metric-Palatini gravity
European Physical Journal C: Particles and Fields, 2023 In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics.
S. Golsanamlou, K. Atazadeh, M. Mousavi
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Covariant Space-Time Line Elements in the Friedmann–Lemaitre–Robertson–Walker Geometry
Axioms, 2022 Most quantum gravity theories quantize space-time on the order of Planck length (ℓp ). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over ...
David Escors, Grazyna Kochan
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Further results on q-Lie groups, q-Lie algebras and q-homogeneous spaces
Special Matrices, 2021 We introduce most of the concepts for q-Lie algebras in a way independent of the base field K. Again it turns out that we can keep the same Lie algebra with a small modification.
Ernst Thomas
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Geodesic vectors of square metrics on 5- dimensional generalized symmetric spaces [PDF]
ریاضی و جامعهIn this paper, we consider the $(\alpha, \beta)$-metric $F=\frac{(\alpha + \beta)^2}{\alpha}$ along with the function $\phi$ with the definition of $\phi(s)=1+2s+s^2$, which is known as a square metric, on 5-dimensional generalized symmetric spaces. Then
Dariush Latifi, Milad Zeinali
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