Global hypoellipticity of sums of squares on compact manifolds

Abstract

In this work, we present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on a product of compact Riemannian manifolds $T\times G$, where $G$ is also a Lie group. These new conditions involve the global hypoellipticity of a system of vector fields and are weaker than Hörmander's condition, at the same time that they generalize the well known Diophantine conditions on the torus. We were also able to provide examples of operators satisfying these conditions in the general setting.

arXiv comment35 pages

References in corpus (1)

• Global regularity and solvability of left-invariant differential systems on compact Lie groups

Cited by in corpus (1)

• Global solutions for systems of strongly invariant operators on closed manifolds