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

Omori, Hideki; Kobayashi, Takao

Hokkaido Math. J. 28, No. 3, 613-633 (1999).

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.

Reviewer: P.Popivanov (Sofia)

MSC:

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

Keywords:

horizontal Laplacians