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For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we firstdefine a generalization of the well known Blaschke curvature of the dimensiontwo, which vanishes iff the web has the maximum possible rank which is one.But, contrary to the dimension two where all 3-webs of rank one are locallyisomorphic, we prove that there are infinitely many classes of isomorphism forgerms of 4-webs by curves of rank one in the dimension three : we provide aprocedure for building all of them, up to isomorphism, and give examples ofinvariants of these classes allowing in particular to distinguish the so-calledquadrilateral webs among them.

Etude des (n+1)-tissus de courbes en dimension n