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Results tagged with sg.symplectic-geometry
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user 605
Hamiltonian systems, symplectic flows, classical integrable systems
3
votes
In a contact manifold, is every tranverse 1-foliation given by some Reeb vector field?
I think the answer is no.
Since a Reeb vector field must be in the Kernel of $d\alpha$, the foliation would need
to have very special holonomy. The restriction of $d \alpha$ to transversals would
gi …
- 8,828
1
vote
Can a Lagrangian submanifold of ${\mathbb R}^{2n}$ be dense ($n>1$)?
This is more a remark than an answer.
The typical solution of the typical polynomial ODE is uniformized by the Poincaré disc not by the complex line.
Indeed, after the work of McQuillan, it is know …
- 8,828
13
votes
Complex hypersurface in complex projective space
A more general version of the question made by the OP is the following
Question. Let $H_1$ and $H_2$ be two smooth connect hypersurfaces in a projective manifold $X$. Suppose $H_1$ is homologous to …
- 8,828
4
votes
Obstructions to being a hyperplane section or a fibre of a Lefschetz pencil
Your question is related to the problem of the existence of non-trivial extensions of subvarieties $X \subset \mathbb P^N$ to $\mathbb P^{N+1}$. An extension of $X$ is just a subvariety $Y$ of $\mathb …
- 8,828