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Titlebook: Exterior Differential Systems and Equivalence Problems; Kichoon Yang Book 1992 Springer Science+Business Media Dordrecht 1992 differential

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Embeddings of G-structures,Several applications of exterior differential system theory in differential geometry are given in this chapter. The theme is that of embedding a given G-structure. To be more precise, given an abstract G-structure we wish to find a submanifold f in the model space so that the structure induced by f coincides with the given one.
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Overview: 978-90-481-4118-0978-94-015-8068-7
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https://doi.org/10.1007/978-981-99-5628-9 (Σ, ω) is quasi-linear, the fibers of .(Σ, ω) → M are affine spaces, hence irreducible. Consequently, none of the complications of the multiple component case occurs; moreover, the question of involutivity reduces in large measure to linear algebra. The symbol relations of a quasi—linear system are given at the end of §1.
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he sum . is the maximum dimension of the polar systems of the E.’s in G. (X). We then have the following basic result: the irreducible component X contains an ordinary integral element if and only if .. At the end of §1 we give a proof of Cartan’s test using this result.
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Involution and Prolongation,he sum . is the maximum dimension of the polar systems of the E.’s in G. (X). We then have the following basic result: the irreducible component X contains an ordinary integral element if and only if .. At the end of §1 we give a proof of Cartan’s test using this result.
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Quasi-Linear Pfaffian Differential Systems, (Σ, ω) is quasi-linear, the fibers of .(Σ, ω) → M are affine spaces, hence irreducible. Consequently, none of the complications of the multiple component case occurs; moreover, the question of involutivity reduces in large measure to linear algebra. The symbol relations of a quasi—linear system are given at the end of §1.
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