Almost nef regular foliations and Fujita's decomposition of reflexive sheaves

In this paper, we study almost nef regular foliations. We give a structure theorem of smooth projective variety $X$ with an foliation $\mathcal{F}$: admits morphism $f: X \rightarrow Y$ rationally connected fibers such that $\mathcal{F}$ is pullback numerically flat on $Y$. Moreover, $f$ characterized as relative MRC fibration algebraic part $\mathcal{F}$. As corollary, tangent bundle generically ample. For the proof, generalize Fujita's decomposition theorem. by-product, show reflexive hull $f_{*}(mK_{X/Y})$ direct sum hermitian vector and ample sheaf for any fiber space $f : Y$. also foliations anti-canonical bundles.