On anisotropic invariants of a symmetric tensor: crystal classes, quasi-crystal classes and others

摘要

This paper is concerned with invariants of a symmetric second-order tensor relative to crystal classes and quasi-crystal classes and some non-continuous infinite orthogonal subgroups. Simple irreducible functional bases in unified forms, each of which consists of eight polynomial invariants only, are presented for all kinds of finite subgroups of the maximal transverse isotropy group: D-och, except the subgroups of the orthotropy group D-2h Results are also provided for other kinds of orthogonal subgroups including icosahedral quasi-crystal classes, etc. For the trigonal, tetragonal and hexagonal crystal classes without two-fold axes, the results given here are even more compact than the corresponding results recently derived by this author. For all non-crystal classes except the transverse isotropy groups, the presented results are the first ones. [References: 40]