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A differential form $ \omega$ is a section of the exterior algebra $\Lambda^* T^* X$ of a cotangent bundle,
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When is a given matrix of two forms a curvature form?
Let's assume we are working over $\mathbb{R}^n$ (but feel free to change to domain to answer the question). I wish to know if the equation $F = dA + A \wedge A$ can be solved for a matrix of 1-forms $ …