Additions to the paper: Steady circulation-preserving motions with certain conditions on the Rivlin-Erickson tensors \(A_ 1\) and \(A_ 2\) (Q1264054)

As extension of the authors paper [reviewed above (Zbl 0688.76006)] the author proves that the common proper vectors of \(A_ 1\) and \(A_ 2\) must be spatially constant vectors; their vectorlines must be parallel straight lines forming a Cartesian system. For the irrotational motion \(A_ 1=2\quad \text{grad} \nu.\) Thus \(\text{grad} \nu\) is a symmetric tensor with constant, distinct and non-vanishing proper numbers and spatially constant proper vectors. We call these irrotational motions steady extensions. We thus deduce the following stronger result: The only steady isochoric circulation-preserving motions for which the proper numbers of \(A_ 1\) are constant, distinct and non-vanishing, and for which \(A_ 1\) and \(A_ 2\) have common proper vectors, are steady extensions.