Zobrazeno 1 - 10
of 519
pro vyhledávání: '"Zeghib A"'
We present the classification of geodesic completeness on the pseudo-homothetic Lie group of dimension 3. In particular, we exhibit a family of complete metrics such that all geodesics have bounded velocity. As an application, we show that the set of
Externí odkaz:
http://arxiv.org/abs/2410.20612
Autor:
Mehidi, Lilia, Zeghib, Abdelghani
This paper provides an introduction to Kundt spaces, clarifying several important properties, many of which are typically scattered across the mathematical literature or presented without explicit reference to Kundt terminology. While not exhaustive,
Externí odkaz:
http://arxiv.org/abs/2410.12531
We study compact complex manifolds $M$ admitting a conformal holomorphic Riemannian structure invariant under the action of a complex semi-simple Lie group $G$. We prove that if the group $G$ acts transitively and essentially, then $M$ is conformally
Externí odkaz:
http://arxiv.org/abs/2405.02527
Plane waves are a special class of Lorentzian spaces with a parallel null vector field. They are of great importance in Geometry (e.g. Lorentzian holonomy) and in Physics (General Relativity as well as alternative gravity theories). Our contribution
Externí odkaz:
http://arxiv.org/abs/2311.07459
We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a connected subgro
Externí odkaz:
http://arxiv.org/abs/2309.14955
Publikováno v:
Trans. Amer. Math. Soc., 377(8):5837-5862, 2024
For each left-invariant semi-Riemannian metric $g$ on a Lie group $G$, we introduce the class of bi-Lipschitz Riemannian Clairaut metrics, whose completeness implies the completeness of $g$. When the adjoint representation of $G$ satisfies an at most
Externí odkaz:
http://arxiv.org/abs/2308.16513
Publikováno v:
Geom. Funct. Anal. (2024)
We construct compact Lorentz manifolds without closed geodesics.
Comment: Minor edits. To appear in GAFA
Comment: Minor edits. To appear in GAFA
Externí odkaz:
http://arxiv.org/abs/2307.16810
We study compact connected pseudo-Riemannian manifolds $(M,g)$ on which the conformal group $\operatorname{Conf}(M,g)$ acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of $\operatorname{Conf}(M,g)$
Externí odkaz:
http://arxiv.org/abs/2305.18868
We revisit the classification of Lorentz homogeneous spaces of dimension 3, fixing statements in the literature and relaxing usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmet
Externí odkaz:
http://arxiv.org/abs/2210.11439
Autor:
Mehidi, Lilia, Zeghib, Abdelghani
Brinkmann Lorentz manifolds are those admitting an isotropic parallel vector field. We prove geodesic completeness of the compact and also compactly homogeneous Brinkmann spaces. We also prove, partially, that their parallel vector field generates an
Externí odkaz:
http://arxiv.org/abs/2205.07243