ON WEAKLY ISOTROPIC TENSORS

We define and characterize weakly isotropic tensors in terms of proper ties of invariance with respect to some sets of rotations, for instanc e, those in the cubic group. Hence, in particular, we characterize wea kly isotropic tensors which are isotropic or skew-isotropic depending on whether their order is even or odd, respectively. Restricting our a ttention to tensors of order less than or equal to 7, we characterize a minimal set of rotations such that the invariance with respect to it implies the property of weak isotropy. Then we show that any weakly i sotropic tensor of order 7 can be represented in terms of 36 independe nt arbitrary scalars. This number of independent scalars is minimal, i n the sense that any representation for such a tensor involves at leas t 36 scalars. We produce two such minimal representations, firstly by finding a suitable choice of independent components, in terms of which we express the remaining tensor components. Secondly, we find 36 line arly independent weakly isotropic tensors which are products of a Ricc i symbol with two Kronecker symbols and are such that any other weakly isotropic tensor can be expressed as a linear combination of them.