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

MathSciNet review:
961601

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Abstract: To every positive -quadratic differential form defined on an oriented two manifold is associated a pair of transversal one-dimensional -foliations with common singularities. An open set of positive -quadratic differential forms with structural stable associated foliations is characterized and it is proved that this set is dense in the space of positive -quadratic differential forms with -topology. Also a realization theorem is established.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1988-0961601-4

Article copyright:
© Copyright 1988
American Mathematical Society