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Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.
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Understanding exterior differential systems
Let $M$ be an $n$-dimensional smooth manifold. An exterior differential system on $M$ is by definition a graded ideal $\mathcal{I}\subset \Omega^{\bullet}(M)$ in the ring $\Omega^{\bullet}(M)$ of diff …