Quasiregular curves and cohomology

Let be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular ‐curve with infinite energy. We prove that, if the de Rham class of is nonzero and a finite sum of nontrivial products, then there exists a nontrivial graded algebra homomorphism from the de Rham algebra of to the exterior algebra . As an application, we give examples of pairs , where is a closed manifold and is a closed ‐form for , for which every quasiregular ‐curve is constant.