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Regularity of mappings of $ G$-structures of Frobenius type


Author: Chong-Kyu Han
Journal: Proc. Amer. Math. Soc. 106 (1989), 127-137
MSC: Primary 58A15; Secondary 53C10
DOI: https://doi.org/10.1090/S0002-9939-1989-0953743-0
MathSciNet review: 953743
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Abstract: A notion of Frobenius type for a $ G$-structure is defined. It is shown that a mapping $ f$ between $ {C^\infty }({\text{resp}}{\text{.}}{C^\omega })$ manifolds with a $ G$-structure of the Frobenius type is $ {C^\infty }({\text{resp}}{\text{.}}{C^\omega })$ if $ f \in {C^k}$, where the integer $ k$ depends on the order of the Frobenius type. It is also shown that a $ G$-structure of finite order is of the Frobenius type.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0953743-0
Keywords: $ G$-structures, infinitesimal automorphisms, Frobenius type, Lie algebras of finite order, CR structures
Article copyright: © Copyright 1989 American Mathematical Society

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