Regularity of mappings of 𝐺-structures of Frobenius type

Han, Chong-Kyu

doi:10.1090/S0002-9939-1989-0953743-0

Regularity of mappings of $G$-structures of Frobenius type
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Proc. Amer. Math. Soc. 106 (1989), 127-137 Request permission

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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