Search results for "Contact manifold"
showing 2 items of 2 documents
Heisenberg quasiregular ellipticity
2016
Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group $\mathbb{H}$. As an application, we show that a link complement $S^3\backslash L$ has a sub-Riemannian metric admitting such a mapping only if $L$ is empty, the unknot or Hopf link. In the converse direction, if $L$ is empty, a specific unknot or Hopf link, we construct a quasiregular mapping from $\mathbb{H}$ to $S^3\backslash L$. The main result is obtained by translating a growth condition on $\pi_1(M)$ into the existence of a supersolution to the $4$-harmonic…
Star calculus on Jacobi manifolds
2002
Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.