Results 51 to 60 of about 1,765 (105)
Magnetic Trajectories on 2-Step Nilmanifolds
The Journal of Geometric Analysis, 2023 The aim of this work is the study of magnetic trajectories on nilmanifolds. The magnetic equation is written and the corresponding solutions are found for a family of invariant Lorentz forces on a 2-step nilpotent Lie group equipped with a left-invariant metric.
Ovando, Gabriela Paola, Subils, Mauro
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Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical
Mathematische Nachrichten, Volume 297, Issue 12, Page 4705-4729, December 2024.Abstract In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of J$J$‐invariant nilradical and non‐J$J$‐invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided.
Beatrice Brienza, Anna Fino
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Gradings on Lie algebras with applications to infra-nilmanifolds
, 2016 In this paper, we study positive as well as non-negative and non-trivial gradings on finite dimensional Lie algebras. We give a different proof that the existence of such a grading on a Lie algebra is invariant under taking field extensions, a result ...
Deré, Jonas
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Structure of the Kuranishi spaces of pairs of Kähler manifolds and polystable Higgs bundles
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3581-3600, December 2024.Abstract Let X$X$ be a compact Kähler manifold and (E,∂¯E,θ)$(E,\overline{\partial }_E,\theta)$ be a Higgs bundle over it. We study the structure of the Kuranishi space for the pair (X,E,θ)$(X, E,\theta)$ when the Higgs bundle admits a harmonic metric or equivalently when the Higgs bundle is polystable and the Chern classes are 0.
Takashi Ono
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The R∞ property for nilpotent quotients of surface groups
Transactions of the London Mathematical Society, Volume 3, Issue 1, Page 28-46, 2016., 2016 A group G is said to have the R∞ property if, for any automorphism φ of G, the number R(φ) of twisted conjugacy classes (or Reidemeister classes) is infinite. It is well known that when G is the fundamental group of a closed surface of negative Euler characteristic, it has the R∞ property.
Karel Dekimpe, Daciberg L. Gonçalves
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Small‐scale distribution of linear patterns of primes
Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract Let Ψ=(ψ1,⋯,ψt):`Zd→Rt$\Psi =(\psi _1,\hdots, \psi _t):`\mathbb {Z}^d\rightarrow \mathbb {R}^t$ be a system of linear forms with finite complexity. In their seminal paper, Green and Tao showed the following prime number theorem for values of the system Ψ$\Psi$: ∑x∈[−N,N]d∏i=1t1P(ψi(x))∼(2N)d(logN)t∏pβp,$$\begin{equation*} \sum _{x\in [-N,N]^d}
Mayank Pandey, Katharine Woo
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A Restriction for Singularities on Collapsing Orbifolds
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Every point p in an orbifold X has a neighborhood that is homeomorphic to Gp∖Br(0), where Gp is a finite group acting on Br(0) ⊂ ℝn, so that Gp(0) = 0. Assume X is a Riemannian orbifold with isolated singularities that is collapsing, that is, X admits a sequence of metrics gi with uniformly bounded curvature, so that, for any x ∈ X, the volume of B1(x),
Yu Ding +3 more
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The Length of Harmonic Forms on a Compact Riemannian Manifold
, 2003 We study $n$ dimensional Riemanniann manifolds with harmonic forms of constant length and first Betti number equal to $n-1$ showing that they are 2-steps nilmanifolds with some special metrics.
Nagy, Paul-Andi, Vernicos, Constantin
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Inhomogeneous deformations of Einstein solvmanifolds
Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.Abstract For each non‐flat, unimodular Ricci soliton solvmanifold (S0,g0)$(\mathsf {S}_0,g_0)$, we construct a one‐parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by S0$\mathsf {S}_0$. The orbits of this action are hypersurfaces homothetic to (S0,g0)$(\mathsf {S}_0,g_0)$.
Adam Thompson
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An inverse theorem for the Gowers U^{s+1}[N]-norm
, 2011 We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s [-1,1] is a function with || f ||_{U^{s+1}[N]} > \delta then there is a bounded-complexity s-step nilsequence F(g(n)\Gamma) which ...
Green, Ben, Tao, Terence, Ziegler, Tamar
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