Classification of differential (n — 1)-forms on an n-dimensional manifold with boundary
In this paper we classify differential n-forms and (n — 1)-forms on an n-dimentional manifold with boundary with respect to the equivalence defined by pullback via a diffeomorphism, which preserves the manifold together with its boundary. We present a complete list of the locally stable n-forms. We also classify all the stable (n — 1)-forms, provided a kernel of these forms meets the boundary transversally. We show that a 1-form on a 2-dimensional manifold, which does not satisfy the above condition, is not locally stable.
KeywordsVector Field Smooth Function Stable Mapping Symplectic Structure Smooth Hypersurface
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