Lie algebra on the transverse bundle of a decreasing family of foliations (Q1049008)

In [\textit{J. Lehmann-Lejeune}, C. R. Acad. Sci., Paris, Sér. I 295, 495--498 (1982; Zbl 0538.57012)], a tensor structure \(J\) with \(J^2=0\) was defined satisfying a certain equation on \(V\), the transverse bundle to a given foliation. This led to consideration of the Lie algebra of vector fields on an open set whose Lie derivative kills \(J\) (so that \(J\) is then preserved along the flows of the vector fields). The kernel of \(J\) on the open set was then characterized in terms of this Lie algebra. The author of the present paper generalizes these results to the situation of \(k\) foliations obeying \(F_1 \supset \cdots \supset F_k\) with codimensions \(p_1,p_1+p_2,p_1+p_2+p_3, \dots\).