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.
Cite this paper
M. Czarnecki and S. Walczak, "De Sitter Space as a Computational Tool for Surfaces and Foliations," American Journal of Computational Mathematics, Vol. 3 No. 1, 2013, pp. 1-5. doi: 10.4236/ajcm.2013.31A001.
 M. Czarnecki and P. Walczak, “Extrinsic Geometry of Foliations,” World Scientific, Singapore, 2006, pp. 149-167.
 M. Badura and M. Czarnecki, “Recent Progress in Geometric Foliation Theory,” World Scientific, Singapore, 2013.
 J. O’Hara, “Energy of Knots and Conformal Geometry,” World Scientific, Singapore, 2003.
 R. Langevin and P. G. Walczak, “Conformal Geometry of Foliations,” Geometriae Dedicata, Vol. 132, No. 1, 2008, pp. 135-178. doi:10.1007/s10711-007-9213-1.
 A. Bartoszek, R. Langevin and P. G. Walczak, “Special Canal Surfaces of S3,” Bulletin of the Brazilian Mathematical Society New Series, Vol. 42, No. 2, 2011, pp. 301-320.
 R. Langevin and P. G. Walczak, “Canal Foliations of S3,” Journal of the Mathematical Society of Japan, Vol. 64, No. 2, 2012, pp. 659-682.
 M. Czarnecki and R. Langevin, “Totally Umbilical Foliations on Hyperbolic Spaces,” in Press.
 M. Czarnecki and M. LuZynczyk, “Umbilical Routes along Gedesics in Hyperbolic Spaces, in Press.