Globally analytic hypoelliptic vector fields on compact surfaces

Bergamasco, Adalberto; Zani, Sérgio

doi:10.1090/S0002-9939-07-09097-1

Globally analytic hypoelliptic vector fields on compact surfaces
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by Adalberto P. Bergamasco and Sérgio Luís Zani

Proc. Amer. Math. Soc. 136 (2008), 1305-1310

DOI: https://doi.org/10.1090/S0002-9939-07-09097-1

Published electronically: November 28, 2007

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Abstract:

We present a characterization of the global analytic hypoellipticity of a complex, non-singular, real analytic vector field defined on a compact, connected, orientable, two-dimensional, real analytic manifold. In particular, we show that such vector fields exist only on the torus.

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