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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Positive quadratic differential forms and foliations with singularities on surfaces


Author: Víctor Guíñez
Journal: Trans. Amer. Math. Soc. 309 (1988), 477-502
MSC: Primary 57R30; Secondary 49F05, 58A10, 58F99
DOI: https://doi.org/10.1090/S0002-9947-1988-0961601-4
MathSciNet review: 961601
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Abstract: To every positive $ {C^r}$-quadratic differential form defined on an oriented two manifold is associated a pair of transversal one-dimensional $ {C^r}$-foliations with common singularities. An open set of positive $ {C^r}$-quadratic differential forms with structural stable associated foliations is characterized and it is proved that this set is dense in the space of positive $ {C^\infty }$-quadratic differential forms with $ {C^2}$-topology. Also a realization theorem is established.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0961601-4
Article copyright: © Copyright 1988 American Mathematical Society