Deformations of homogeneous foliations

Let X be a simply connected compact homogeneous Kähler manifold, b₂(X) = 1, and let E be a homogeneous vector foliation on X. A complete effective family of deformations of a holomorphic vector foliation E , this family parametrized by a neighborhood of zero in H¹(X,o End ), is constructed.Translated from Matematicheskie Zametki, Vol. 3, No. 6, pp. 651–656, June, 1968.The author is indebted to A. L. Onishchik for his assistance and interest in the completion of the paper.