ON A NECESSARY CONDITION OF LOCAL INTEGRABILITY FOR COMPLEX VECTOR FIELD IN R~2

摘要

Let X be a non-solvable C~∞ complex vector field in R~2 satisfying certain condi- tions. A necessary condition for the equation X_μ = 0 to have a solution μ such that dμ≠0 near the origin and one for the Xμ=0 to admit a solution μ such that dμ≠0 in any suffi- ciently small neighborhood of the origin are given. These are expressed by making use of an estimate.