Abstract

We consider a space X of constant curvature (Euclidean, elliptic, and hyperbolic space, and the sphere). The set of isometries of X transforming a surface such that it touches a second surface is called the configuration space of surface–surface contact. We investigate when this subset of Isom(X) is an immersed submanifold (which depends on the principal curvatures of the surfaces involved), and when it is an embedded submanifold (which depends on the ‘size’ and ‘shape’ of the given surfaces).

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