THE EQUATION 2I(PARTIAL-DERIVATIVE)OVER-B AR-PARTIAL-DERIVATIVE-F=BETA FOR (1,1)-TENSOR FIELDS

Consider, on a real or complex manifold, a 2-form beta and a (1, 1)-te nsor field J whose Nijenhuis torsion vanishes, such that P-J = 0, wher e P-J is like in [4] (for example, that is the case if J can be locall y written with constant coefficients). In this Note we give a necessar y and sufficient condition for the local existence, on the regular ope n set, of a function f such that d(df circle J) = beta, where (df circ le J)(X) = df(JX). When J(2) = -Id we find the equation 2i partial der ivative partial derivative f = beta.