Nonisoclinic $2$-codimensional $4$-webs of maximum $2$-rank
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- by Vladislav V. Goldberg PDF
- Proc. Amer. Math. Soc. 100 (1987), 701-708 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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