Generalization of Steiner’s Porism via Poncelet’s Theorem

In this paper, motivated by Poncelet’s theorem, we give a generalization of Steiner’s porism for spheres in En. First, we define Steiner chains for n given spheres. Using the three-inversion theorem, we prove that there is a 1-parameter subgroup of Möbius transformations preserving these n spheres. By applying the elements of this subgroup to a Steiner chain, we will get a 1-parameter family of Steiner chains such that the closedness of them are equivalent.