Locally Stable Singularities for Positive Quadratic Differential Forms

Every positive C∞-quadratic differential form defined on an oriented surface has two transverse C∞-one-dimensional foliations with common singularities associated to it. In this article we give conditions, at the first jet of a positive C∞-quadratic differential form at a singular point, for local stability. This result implies a characterization of the structurally stable positive C∞-quadratic differential form defined on an oriented and compact smooth surface with the C2-Whitney topology.