What is the definition of a Lipschitz-regular 1-form on a riemannian manifold?
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How would you define a (locally) Lipschitz function? Try the same with forms. – Moishe Kohan Aug 29 '14 at 20:13
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@studiosus I would define for functions using the metric on the manifold and the metric on $\mathbb{R}$, but with forms i don't know which metric to use on the cotangent bundle. – Pedro Aug 29 '14 at 20:58
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There is a natural metric on the tangent bundle, which is naturally identified with the cotangent bundle for Riemannian manifolds. – Aug 29 '14 at 22:15
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First of all, I assume that you are asking about forms which are only locally Lipschitz, otherwise the answer will be different (the function $x^2$ on the real line is only locally Lipschitz). Then the simplest thing to do is to write your form in local coordinates and require all the component functions to be locally Lipschitz. There are alternative equivalent definitions, where you put your favorite Riemannian metric (which one does not matter) on tensor powers of the tangent bundle and think of forms as locally Lipschitz sections.
Moishe Kohan
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