Global properties of a class of overdetermined systems

被引:16
作者
Bergamasco, AP
Nunes, WVL
Zani, SL
机构
[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil
[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
关键词
global solvability; analytic singularities; pseudoperiodic functions; locally integrable structures; stationary phase;
D O I
10.1016/S0022-1236(02)00055-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider an overdetermined system of complex vector fields on the three-dimensional torus which is naturally associated to a real analytic, closed 1-form on the two-dimensional torus. By means of a detailed study of the geometry of level sets of a primitive of the pull-back of the 1-form via the universal covering, we prove that a necessary condition for the system to be globally solvable, in the non-exact case, is that each connected component of the critical set has a point at which the local primitives of the 1-form are open maps. When this condition is violated we also construct global solutions to the inhomogenous equations having analytic singularities. (C) 2002 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:31 / 64
页数:34
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