Abelian equations and rank problems for planar webs
We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincar´e’s theorem: a planar 4- web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs of rank two and one and prove that in general such webs are not linearizable. This solves the Blaschke problem “to find invariant conditions for a planar 4-web to be of rank 1 or 2 or 3”. Finally, we find invariant characterization of planar 5-webs of maximum rank and prove than in general such webs are not linearizable.
Dette er forfatternes aksepterte versjon.
PublisherAllerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
CitationRussian Mathematics (Iz VUZ) DOI: 10.3103/S1066369X07100039
MetadataShow full item record
The following license file are associated with this item: