Lipschitz continuous invariant forms for algebraic Anosov systems (Q609749)

Let \(M\) be a compact, locally symmetric space with negative sectional curvature. The authors establish the following property of the geodesic flow \(\phi^t\) on \(M\): If \(A\) is a Lipschitz continuous 1-form such that \(dA\) is \(\phi^t\)-invariant, then \(A\) is \(C^\infty\), and \(dA\) is a constant multiple of the exterior derivative of the canonical 1-form of \(\phi^t\). They also study properties of invariant 2-forms for hyperbolic automorphisms of tori and infranilmanifolds and their suspensions.