an:05233269
Zbl 1139.35038
Bergamasco, Adalberto P.; Zani, S??rgio Lu??s
Globally analytic hypoelliptic vector fields on compact surfaces
EN
Proc. Am. Math. Soc. 136, No. 4, 1305-1310 (2008).
00215864
2008
j
35H10 58J99
Liouville numbers; sheaf cohomology; Sussmann orbits
This paper deals with complex, non-singular, real analytic vector field \(L\) defined on a compact, connected, orientable, two-dimensional, real analytic manifold \(M\). The authors call \(L\) vector field of type I if \(\text{Re\,}L\), \(\text{Im\,}L\) are linearly independent everywhere on \(M\). Otherwise, \(L\) is called vector field of type II. A complete characterization of the global analytic hypoelliptic vector fields of types I and II is given. It follows from their results that in the class of compact surfaces \(M\), globally analytic hypoelliptic vector fields can exist only if \(M\) is real analytically diffeomorphic to the two-torus \(\mathbb{T}^2\).
Petar Popivanov (Sofia)