Nijenhuis geometry of parallel tensors
Nijenhuis geometry of parallel tensors
A tensor -- meaning here a tensor field $\Theta$ of any type $(p,q)$ on a manifold -- may be called integrable if it is parallel relative to some torsion-free connection. We provide analytical and geometric characterizations of integrability for differential $q$-forms, $q=0,1,2,n-1,n$ (in dimension $n$), vectors, bivectors, symmetric $(2,0)$ and …