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.