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Rank problems for webs $$W(d,2,r)$$. (English) Zbl 0789.53008
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 317-357 (1992).
A detailed account of rank problems for $$(d,2,r)$$-webs is given. In particular, an introduction to general web theory is provided and the following theorems are proved: webs $$W(d,2,r)$$ of maximum $$r$$-rank are almost Grassmannizable; an almost Grassmannizable web $$AGW(d,2,2)$$, where $$d > 4$$, is of maximum 2-rank if and only if it is algebraizable.
For the entire collection see [Zbl 0764.00002].

##### MSC:
 53A60 Differential geometry of webs
##### Keywords:
webs; rank problems; Grassmannizable web