Split distributions on Grassmann manifolds and smooth quadric hypersurfaces

Abstract: This work is dedicated to studying holomorphic distributions on Grassmann manifolds and smooth quadric hypersurfaces. In special, we prove, under certain conditions, when the tangent and conormal sheaves of a distribution splits as a sum of line bundle on these manifolds, generalizing the previous works on Fano threefolds and $\mathbb{P}^{n}$. We finish the paper with result about the connectivity of the singular locus of the distribution.