Multidimensional (n+1)-Webs with Reduct Reducible Subwebs

Details Multidimensional (n+1)-Webs with Reduct Reducible Subwebs Multidimensional (n+1)-Webs with Reduct Reducible Subwebs

2000-10-17

arxiv.org/abs/math/0010178v1

Rend. Sem. Mat. Messina, Ser. II 21 (1999) no. 6 27-32

Mathematics

Differential Geometry

LaTeX, 4 pages

Scientific paper

We find three characterizations for a multidimensional (n+1)-web W possessing a reduct reducible subweb: its closed form equations, the integrability of an invariant distribution associated with W, and the relations between the components of its torsion tensor. In the case of codimension one, the latter criterion establishes a relation with solutions of a system of nonlinear second-order PDEs. Some particular cases of this system were considered by Goursat in 1899.

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