Abstract
It is shown that if a motion is such that the first two Rivlin-Ericksen tensors A1 and A2 have the same unit proper vectors, and A1 has distinct proper numbers, then all the Rivlin-Ericksen tensors A1, A2, ..., An, ... have the same proper vectors. If further this motion is steady and isochoric, then the product of velocity components corresponding to the unit proper vectors, assumed to be non-vanishing, and the product of the abnormalities of the vector fields of the proper vectors, also assumed to be non-vanishing, each bear a constant value along a streamline. If A1 has a pair of equal proper numbers the first statement remains true, but the results for steady isochoric motions will not necessarily hold.
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