Positive quadratic differential forms and foliations with singularities on surfaces

Guíñez, Víctor

doi:10.1090/S0002-9947-1988-0961601-4

Positive quadratic differential forms and foliations with singularities on surfaces
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by Víctor Guíñez PDF

Trans. Amer. Math. Soc. 309 (1988), 477-502 Request permission

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.

References

Estabilidade estructural para campos de linhas em variedades

dimensionais

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