Details

Autor(en) / Beteiligte

• Hounie, J.
• Zugliani, G.

Titel

Tube Structures of Co-rank 1 with Forms Defined on Compact Surfaces

Ist Teil von

• The Journal of geometric analysis, 2021-03, Vol.31 (3), p.2540-2567

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2021

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the global solvability of a locally integrable structure of tube type and co-rank 1 by considering a linear partial differential operator L associated to a general complex smooth closed 1-form c defined on a smooth closed n -manifold. The main result characterizes the global solvability of L when n = 2 in terms of geometric properties of a primitive of a convenient exact pullback of the form Im ( c ) as well as in terms of homological properties of Re ( c ) related to small divisors phenomena. Although the full characterization is restricted to orientable surfaces, some partial results hold true for compact manifolds of any dimension, in particular, the necessity of the conditions, and the equivalence when Im ( c ) is exact. We also obtain informations on the global hypoellipticity of L and the global solvability of L n - 1 —the last non-trivial operator of the complex when M is orientable.