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Recent years have shown that the usual generalizations of taut foliations to higher dimensions, based only on topological concepts, do not yield a theory comparable in richness to the $3$-dimensional one. The aim of this article is to prove that stro
Externí odkaz:
http://arxiv.org/abs/2410.07090
Autor:
Cardona, Robert, Gironella, Fabio
In this paper, we study confoliations in dimensions higher than three mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkr\"uger-Wendl's bordered Legendrian open book, an object that obstructs the weak symple
Externí odkaz:
http://arxiv.org/abs/2410.06918
Autor:
Aydin, Cengiz
It is well-known that the planar and spatial circular restricted three-body problem (CR3BP) is of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea extended Hill's approach in the CR3BP to the spatial equila
Externí odkaz:
http://arxiv.org/abs/2407.06927
Autor:
Cieliebak, Kai
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2406.02985
We study the global topology of the space $\mathcal L$ of loops of contactomorphisms of a non-orderable closed contact manifold $(M^{2n+1}, \alpha)$. We filter $\mathcal L$ by a quantitative measure of the ``positivity'' of the loops and describe the
Externí odkaz:
http://arxiv.org/abs/2406.01148
Autor:
Manev, Mancho
Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here we consider a special cl
Externí odkaz:
http://arxiv.org/abs/2405.14364
Autor:
Hind, Richard
An integral product Lagrangian torus in the standard symplectic $\mathbb{C}^2$ is defined to be a subset $\{ \pi|z_1|^2 = k, \, \pi|z_2|^2 =l \}$ with $k,l \in \mathbb{N}$. Let $\mathcal{L}$ be the union of all integral product Lagrangian tori. We co
Externí odkaz:
http://arxiv.org/abs/2405.03866
Publikováno v:
J. Phys. A: Math. Theor. 57 (2024) 395204 (31pp)
If $\eta$ is a contact form on a manifold $M$ such that the orbits of the Reeb vector field form a simple foliation $\mathcal{F}$ on $M$, then the presymplectic 2-form $d\eta$ on $M$ induces a symplectic structure $\omega$ on the quotient manifold $N
Externí odkaz:
http://arxiv.org/abs/2404.19560
In this paper we present some quantitative results concerning symplectic barriers. In particular, we answer a question raised by Sackel, Song, Varolgunes, and Zhu regarding the symplectic size of the $2n$-dimensional Euclidean ball with a codimension
Externí odkaz:
http://arxiv.org/abs/2404.19396
Autor:
Chatterjee, Rima, Kegel, Marc
We classify all contact structures with contact surgery number one on the Brieskorn sphere Sigma(2,3,11) with both orientations. We conclude that there exist infinitely many non-isotopic contact structures on each of the above manifolds which cannot
Externí odkaz:
http://arxiv.org/abs/2404.18177