4 problems

Let $M$ be the underlying manifold, let $U^i$ be smooth in $A'$, let $T^{\mu\ldots}_{\nu\ldots}\in D'^{m}_{n(A' o)}(M)$ admit an associated field $A_s(T^{\mu\ldots}_{\nu\ldots})$,…

Let $M$ be the underlying manifold, let $U^i$ be a piecewise smooth tensor field, let the connection belong to $\Gamma^{3}_{S}(M)$, and let…

Let $U^i$ be a piecewise smooth vector field and let $\Gamma^{\mu}_{\nu\alpha}\in\Gamma^{3}_{S}(M)$. Piecewise-smooth covariant-derivative conjecture. Covariant differentiation alo…

Let $M$ be a four-dimensional manifold, let $U^i$ be a vector field that is piecewise smooth and bounded on every compact set in every chart, let…