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Nonisoclinic $ 2$-codimensional $ 4$-webs of maximum $ 2$-rank


Author: Vladislav V. Goldberg
Journal: Proc. Amer. Math. Soc. 100 (1987), 701-708
MSC: Primary 53A60
DOI: https://doi.org/10.1090/S0002-9939-1987-0894441-X
MathSciNet review: 894441
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Abstract: In recent papers, the author has proved that $ 4$-webs $ {\text{W(4,2,2)}}$ of codimension 2 and maximum $ 2$-rank on a $ 4$-dimensional differentiable manifold are exceptional in the sense that they are not necessarily algebraizable, while maximum $ 2$-rank $ 2$-codimensional $ d$-webs $ {\text{W(d,2,2),}}d > 4$, are algebraizable. Examples of exceptional isoclinic webs W(4,2, 2) were given in those papers. In the present paper, the author proves that a polynomial nonisoclinic $ 3$-web $ {\text{W(3,2,2)}}$ cannot be extended to a nonisoclinic $ 4$-web $ {\text{W(4,2,2)}}$ and constructs an example of a nonisoclinic $ 4$-web $ {\text{W(4,2,2)}}$ of maximum $ 2$-rank.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0894441-X
Keywords: Web, rank, nonisoclinic web, maximum rank web, abelian equation, torsion and curvature tensor, basis affinor
Article copyright: © Copyright 1987 American Mathematical Society

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