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wo ist die Frau von Nawalny - MetaGer
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On geodesic orbit nilmanifolds
Yu. G. Nikonorov
https://arxiv.org/abs/2402.17548 https://arxiv.org/pdf/2402.17548

On geodesic orbit nilmanifolds
The paper is devoted to the study of geodesic orbit Riemannian metrics on nilpotent Lie groups. The main result is the construction of continuous families of pairwise non-isomorphic connected and simply connected nilpotent Lie groups, every of which admits geodesic orbit metrics. The minimum dimension of groups in the constructed families is $10$.

This https://arxiv.org/abs/2401.00654 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center
We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_Γ$. We show that, under certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an affine model. As a consequence, we obtain a centralizer rigidity result, classifying all possible centralizers for any $C^{1}-$small perturbation of an irreducible, affine partially hyperbolic map on $X_Γ$. Along the way, we also prove two results of independent intere…

An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds
Karel Dekimpe, Lore De Weerdt
https://arxiv.org/abs/2404.14889 https…

An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds
In [8,9], the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to $n$-valued maps in [4]. In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any $n$-valued affine map on an infra-nilmanifold.

This https://arxiv.org/abs/2401.00654 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center
We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_Γ$. We show that, under certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an affine model. As a consequence, we obtain a centralizer rigidity result, classifying all possible centralizers for any $C^{1}-$small perturbation of an irreducible, affine partially hyperbolic map on $X_Γ$. Along the way, we also prove two results of independent intere…

2.
Nostalgeek fut un échec. Selon les utilisateurs, l'expérience en LER™️ (Lively Emulated Reality), vendue Š prix d'or, ne tenait pas ses promesses de « revivre dans toute l'authenticité du réel » le mieux-avant. Il était passé complètement sous le radar des études de marché que, malgré leur prétendue #nostalgie, la plupart des gens n'avait nullement voyagé ou évolué, ils s'…

LISA Definition Study Report
Monica Colpi, Karsten Danzmann, Martin Hewitson, Kelly Holley-Bockelmann, Philippe Jetzer, Gijs Nelemans, Antoine Petiteau, David Shoemaker, Carlos Sopuerta, Robin Stebbins, Nial Tanvir, Henry Ward, William Joseph Weber, Ira Thorpe, Anna Daurskikh, Atul Deep, Ignacio Fern\'andez N\'u\~nez, C\'esar Garc\'ia Marirrodriga, Martin Gehler, Jean-Philippe Halain, Oliver Jennrich, Uwe Lammers, Jonan Larra\~naga, Maike Lieser, Nora L\"utzgendorf…

LISA Definition Study Report
The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very…

Rigidity of stable Lyapunov exponents for codimension one Anosov covering maps on nilmanifolds
Ruihao Gu, Wenchao Li
https://arxiv.org/abs/2404.04196 https…

Rigidity of stable Lyapunov exponents for codimension one Anosov covering maps on nilmanifolds
Let $Ψ$ be an endomorphism of a nilmanifold $M = N/Γ$. We show that the preimages of a point under $Ψ$ become dense exponentially if and only if $Ψ$ is totally non-invertible, which means $(M, Ψ)$ has no invertible factors of quotients of factors. As an application, let $f$ be a non-invertible Anosov covering map on $M$ with one-dimensional stable bundle, if $f$ has such linear part $Ψ$ and is topologically conjugate to $Ψ$, then every periodic point of $f$ admits the same stable Lyapuno…

This https://arxiv.org/abs/2402.02537 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds
We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is geometrically-Bott-Chern-formal. We also provide some partial results in higher dimensions for nilmanifolds endowed with a class of suitable complex structures. Furthermore, we prove that any Kähler solvmanifold is geometrically formal. Finally, we explicitly construct lattices fo…

This https://arxiv.org/abs/2310.16726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on $p$-Kähler structures on compact quotients of Lie groups
A $p$-Kähler structure on a complex manifold of complex dimension $n$ is given by a $d$-closed transverse real $(p,p)$-form. In the paper we study the existence of $p$-Kähler structures on compact quotients of simply connected Lie groups by discrete subgroups endowed with an invariant complex structure. In particular, we discuss the existence of $p$-Kähler structures on nilmanifolds, with a focus on the case $p =2$ and complex dimension $n = 4$. Moreover, we prove that a $(n-2)$-Kähler almo…