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Maximum 2-rank webs \(AGW(6,3,2)\). (English) Zbl 0735.53011
The maximum 2-rank almost Grassmannizable 6-webs \(AGW(6,3,2)\) of codimension two given on a six-dimensional differentiable manifold \(X^ 6\) are described in pure geometric terms. In this description two types of maximum 2-rank webs \(AGW(6,3,2)\) are distinguished: the simple webs \(AGW(6,3,2)\) (they do not possess transversal subwebs \(W(6,3,1)\) and necessarily have constant basic affinors) and the general webs \(AGW(6,3,2)\) (they admit transversal subwebs \(W(6,3,1)\)). The conditions given in this description are the first known necessary and sufficient conditions for a maximum rank web of codimension higher than one. It follows from these conditions that even almost Grassmannizable webs \(AGW(6,3,2)\) of maximum 2-rank are not necessarily algebraizable.
MSC:
53A60 Differential geometry of webs
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