Zobrazeno 1 - 10
of 2 474
pro vyhledávání: '"53C50"'
Autor:
Montenegro, Pablo, Ovando, Gabriela P.
The aim of this work is the study of geodesics on Lorentzian homogeneous spaces of the form $M=G/\Lambda$, where $G$ is a solvable Lie group endowed with a bi-invariant Lorentzian metric and $\Lambda < G$ is a cocompact lattice. Conditions to assert
Externí odkaz:
http://arxiv.org/abs/2411.14237
We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional nilpotent Lie a
Externí odkaz:
http://arxiv.org/abs/2411.04856
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
From the classical theory of Lie algebras, it is well-known that the bilinear form $B(X,Y)={\rm tr}(XY)$ defines a non-degenerate scalar product on the simple Lie algebra ${\mathfrak{sl}}(n,{\mathbb R})$. Diagonalizing the Gram matrix $Gr$ associated
Externí odkaz:
http://arxiv.org/abs/2410.15478
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity (non-uniformly) elliptic $p$-d'Alembert o
Externí odkaz:
http://arxiv.org/abs/2410.12632
The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the $(1+2)$-Einstein universe, the conformal compactification of Minkowski 3-space realized as the space of oriented null lines through the origin of $\mathbb
Externí odkaz:
http://arxiv.org/abs/2410.10330
Autor:
Hedicke, Jakob, Neeb, Karl-Hermann
An element $g$ of a Lie group is called stably elliptic if it is contained in the interior of the set $G^e$ of elliptic elements, characterized by the property that $\mathrm{Ad}(g)$ generates a relatively compact subgroup. Stably elliptic elements ap
Externí odkaz:
http://arxiv.org/abs/2410.08083
A four dimensional pseudo-Riemannian manifold of signature (2, 2) is called a Walker manifold if it admits a parallel degenerate plane field. In this paper, we study the curvature properties of such a class of four dimensional Walker manifolds. In pa
Externí odkaz:
http://arxiv.org/abs/2410.06445
Autor:
Franco-Grisales, Andrés
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations; that is, rou
Externí odkaz:
http://arxiv.org/abs/2409.17065
Starting from the proof of the $C^0$-inextendibility of Schwarzschild by Sbierski, the past decade has seen renewed interest in showing low-regularity inextendibility for known spacetime models. Specifically, a lot of attention has been paid to FLRW
Externí odkaz:
http://arxiv.org/abs/2409.13799