Results 51 to 60 of about 317 (142)

Periodic points on nilmanifolds and solvmanifolds [PDF]

Pacific Journal of Mathematics, 1994
Let \(M\) be a compact manifold and \(f:M \to M\) a self map on \(M\). For any natural number \(n\), the \(n\)-th iterate of \(f\) is the \(n\)-fold composition \(f^ n:M \to M\). The fixed point set of \(f\) is \(\text{fix} (f)=\{x \in M:f(x)=x\}\). We say that \(x \in M\) is a periodic point of \(f\) is \(x\) is a fixed point of some \(f^ n\) and we ...
openaire   +3 more sources

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
wiley   +1 more source

On the Analytic Structure of Commutative Nilmanifolds [PDF]

The Journal of Geometric Analysis, 2015
In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases, the nilpotent group $N$ has irreducible unitary representations whose coefficients are square integrable modulo ...
openaire   +4 more sources

Expanding maps on 2-step infra-nilmanifolds

, 2002
A C1-endomorphism f:M→M is expanding if for some Riemannian metric on M there exist c>0,λ>1 such that ∥(Df)mv∥⩾cλm∥v∥ for all v∈TM and all integers m>0.An infra-nilmanifold is the quotient of a connected, simply connected nilpotent Lie group G by a ...
Lee, H., Lee, K.B.
core   +1 more source

Analytic torsion of nilmanifolds with (2, 3, 5) distributions

Analysis and Geometry in Metric Spaces
We consider generic rank two distributions on five-dimensional nilmanifolds and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.
Haller Stefan
doaj   +1 more source

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
wiley   +1 more source

Notes on compact nilspaces

Discrete Analysis, 2017
Notes on compact nilspaces, Discrete Analysis 2017:16, 57 pp. This is the second paper in a two-part series. The first paper, [also published in this journal](http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects ...
Pablo Candela
doaj   +1 more source

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
wiley   +1 more source

Invariants of complex structures on nilmanifolds [PDF]

Archivum Mathematicum, 2015
Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [L1], J.
openaire   +4 more sources

Gravitational instantons with quadratic volume growth

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG$\operatorname{ALG}$ and ALG∗$\operatorname{ALG}^*$. Gravitational instantons of type ALG$\operatorname{ALG}$ were previously classified by Chen–Chen.
Gao Chen, Jeff Viaclovsky
wiley   +1 more source