## Global hypoellipticity of subelliptic operators on closed manifolds.(English)Zbl 0942.35050

This paper deals with the global hypoellipticity of a class of linear differential operators acting on a closed manifold $$M$$ (compact, connected manifold without boundary). Roughly speaking the second order operators under consideration are of the type “sums of squares” of smooth, real tangent vector fields on $$M$$. The authors prove a sufficient condition for global hypoellipticity (Theorem 3.3) and illustrate it by several examples, namely the horizontal Laplacians and some operators which do not have infinite-simally transitive points.

### MSC:

 35H20 Subelliptic equations 58J05 Elliptic equations on manifolds, general theory

### Keywords:

horizontal Laplacians
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