Foliations on the open $3$-ball by complete surfaces
When is a manifold a leaf of a complete closed foliation on the open unit ball? We give some answers to this question.
math.GT↗
arXiv subjects
Takashi Inaba
Publications and source records attributed to Takashi Inaba.
Reeb orbits trapped by Denjoy minimal sets
Let $φ$ be any flow on $T^n$ obtained as the suspension of a diffeomorphism of $T^{n-1}$ and let $\mathcal A$ be any compact invariant set of $φ$. We realize $(\mathcal A, φ|_{\mathcal A})$ up to reparametrization as an invariant set of the Reeb flow of a contact form on $\mathbb R^{2n+1}$ equal to the standard contact form outside a compact set and defining the standard contact structure on all of $\mathbb R^{2n+1}$. This generalizes the construction of Geiges, Röttgen and Zehmisch.
math.SG↗
Anosov actions of (n-1)-dimensional Lie groups on n-dimensional manifolds
We show that there are no Anosov actions by (n-1)-dimensional unimodular Lie groups on closed n-dimensional manifolds.
math.DS↗
Normally contracting Lie group actions
We show that there are no normally contracting actions of unimodular Lie groups on closed manifolds.
math.DS↗