Joaquim Tavares | Searcharxiv

arXiv2014

Local and Global Hartogs-Bochner Phenomenon in Tubes

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure codimension. We give necessary and sufficient conditions for the first cohomological group with compact support to be trivial. A such global result was previously obtained only when the supporting manifold was the Euclidean space. Further but canonical work is need to recover the Bochner extension theorem.

math.CV↗

arXiv2010

On The Existence of Globally Solvable Vector Fields in Smooth Manifolds

Let $(\mathrm{M}, ω_{0})$ be a connected paracompact smooth oriented manifold. We establish a necessary and sufficient conditions on Lie subalgebra $\mathfrak{a}$ of $\mathrm{T M}$ such that its orbits becomes diffeomorphic to an open convex set of $\mathbb{R}^{n}$, where $n$ is the orbit dimension.

math.AP↗