Goursat's (n+1)-Webs

Details Goursat's (n+1)-Webs Goursat's (n+1)-Webs

2000-10-17

arxiv.org/abs/math/0010179v1

Rend. Sem. Mat. Messina, Ser. II 21 (1999) no. 6 53-65

Mathematics

Differential Geometry

LaTeX, 8 pages

Scientific paper

We consider the Goursat's (n+1)-webs of codimension one of two kinds on an n-dimensional manifold. They are characterized by the specific closed form equations or by two special relations between components of the torsion tensor of the web. These relations allow us to establish a connection with solutions of two systems of nonlinear second-order PDEs investigated by Goursat in 1899. The integrability conditions of some distributions invariantly associated with both kinds of Goursat's (n+1)-webs are also investigated.

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