Isosymmetric manifolds in form spaces and the normal deformations of polygonal forms (Q1802454)

If the shape of an object is determined by a set of parameters the space of all possible parameter values forms a space \(\mathcal F\). A path in \(\mathcal F\) represents a deformation of the shape. When \(\mathcal F\) is a Euclidean space and a particular shape exhibits symmetry the deformations that preserve this symmetry give rise to a subvariety of \(\mathcal F\). These are the isosymmetric manifolds of the paper's title. The paper gives detailed examples of the concept for polygonal shapes.