AJCM  Vol.3 No.1 A , April 2013
De Sitter Space as a Computational Tool for Surfaces and Foliations
ABSTRACT

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.
References
[1]   M. Czarnecki and P. Walczak, “Extrinsic Geometry of Foliations,” World Scientific, Singapore, 2006, pp. 149-167.

[2]   M. Badura and M. Czarnecki, “Recent Progress in Geometric Foliation Theory,” World Scientific, Singapore, 2013.

[3]   J. O’Hara, “Energy of Knots and Conformal Geometry,” World Scientific, Singapore, 2003.

[4]   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.

[5]   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.

[6]   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. doi:10.2969/jmsj/06420659

[7]   M. Czarnecki and R. Langevin, “Totally Umbilical Foliations on Hyperbolic Spaces,” in Press.

[8]   M. Czarnecki and M. LuZynczyk, “Umbilical Routes along Gedesics in Hyperbolic Spaces, in Press.

 
 
Top