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The \((n+1)\)-webs defined by \(n+1\) surfaces of codimension \(n-1\). (Russian. English summary) Zbl 0547.53007
Itogi Nauki Tekh., Ser. Probl. Geom. 7, 173-195 (1975).
Let \(P_{r+n-1}\) be real \((r+n-1)\)-dimensional projective space. An \((n+1)\)-web is a geometric configuration formed by \(n+1\) r-dimensional surfaces of \(P_{r+n-1}\). It is known that the theory of \((n+1)\)-webs is intimately connected with the theory of n-pseudogroups. In this note fundamental equations and some general properties of \((n+1)\)-webs are established (for example: an \((n+1)\)-web is transversally-geodesic and isoclinal, and so on). Some particular classes of \((n+1)\)-webs (reducible, hexagonal, hexagonal-totally-reducible, parallelizable and so on) are studied and characterized.

53A60 Differential geometry of webs
53A20 Projective differential geometry