The set of all spheres and hyperplanes in the Euclidean space Rn+1 could be identified with the Sitter space Λn+1. All the conformal properties are invariant by the Lorentz form which is natural pseudo-Riemannian metric on Λn+1. We shall study behaviour of some surfaces and foliations as their families using computation in the de Sitter space.
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M. Badura and M. Czarnecki, “Recent Progress in Geometric Foliation Theory,” World Scientific, Singapore, 2013.
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M. Czarnecki and R. Langevin, “Totally Umbilical Foliations on Hyperbolic Spaces,” in Press.
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