Abstract
Let U ⊑ M be a local chart on M and let ω(u, v) be a C r-quadratic differential form: \(a(u,v)d{u^2} + b(u,v)dudv + c(u,v)d{v^2},\) where a, b and c are real-valued functions of class C r. By a positive C r differential 2-form on M one understands a C r-quadratic differential form ω such that for every point x ∈ M, the set ω -1(x)(0) is either
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A union of two transversal lines (such a point is called regular),or
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An isolated point (such a point is called singular).
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References
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© 2001 Springer-Verlag Berlin Heidelberg
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Nikolaev, I. (2001). Positive Differential 2-Forms. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_16
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DOI: https://doi.org/10.1007/978-3-662-04524-4_16
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