Positive quadratic differential forms and foliations with singularities on surfaces

Source abstract

To every positive C r {C^r} -quadratic differential form defined on an oriented two manifold is associated a pair of transversal one-dimensional C r {C^r} -foliations with common singularities. An open set of positive C r {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 ∞ {C^\infty } -quadratic differential forms with C 2 {C^2} -topology. Also a realization theorem is established.