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4-tissus isoclines exceptionnels de codimension deux et de 2-rang maximal. (Isoclinic exceptional two-codimensional four-webs of maximum 2- rank). (French) Zbl 0579.53015

Summary: The author established earlier [C. R. Acad. Sci., Paris, Ser. I 297, 339- 342 (1983; Zbl 0539.53012)] that maximum 2-rank 4-webs W(4,2,2) of codimension 2 on a 4-dimensional manifold are exceptional in the sense that, unlike d-webs W(d,2,2), \(d>4\), they are not necessarily algebraizable. If they are isoclinic, they are almost algebraizable. In this paper a procedure of extension of an isoclinic 3-web W(3,2,2) to an almost algebraizable 4-web W(4,2,2) is given. Examples of isoclinic webs W(3,2,2) which can be extended to an almost algebraizable web W(4,2,2) are presented.

MSC:

53A60 Differential geometry of webs

Citations:

Zbl 0539.53012
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