Abstract
We define a special family of topological two-spheres, which we call ‘rigid spheres’, and prove that there is a four-parameter family of rigid spheres in a generic Riemannian three-manifold (in case of the flat Euclidean three-space these four parameters are: three coordinates of the center and the radius of the sphere). The rigid spheres can be used as building blocks for various (‘spherical’, ‘bispherical’ etc) foliations of the Cauchy space. This way a supertranslation ambiguity may be avoided. Generalization to the full four-dimensional case is discussed. Our results generalize both the Huang foliations (cf [4]) and the foliations used by us (cf [8]) in the analysis of the two-body problem.
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