We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces semisimple algebraic groups discuss how to determine number equivalence classes such structures.

A configuration of a linkage $$\Gamma $$ is possible positioning in $${{\mathbb {R}}}^{d}$$ , and the collection all such forms space $${\mathcal {C}}(\Gamma )$$ . We here introduce notion symmetric linkage, which we identify configurations are geometrically indistinguishable. show that planar polygon has regular cell structure, provide some principles for calculating this give complete descrip...