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
HTML articles powered by AMS MathViewer

by Chong-Kyu Han

Proc. Amer. Math. Soc. 106 (1989), 127-137

DOI: https://doi.org/10.1090/S0002-9939-1989-0953743-0

PDF | 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.

References

M. S. Baouendi, H. Jacobowitz, and F. Trèves, On the analyticity of CR mappings, Ann. of Math. (2) 122 (1985), no. 2, 365–400. MR 808223, DOI 10.2307/1971307
S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
C. K. Han, Analyticity of CR equivalences between some real hypersurfaces in $\textbf {C}^{n}$ with degenerate Levi forms, Invent. Math. 73 (1983), no. 1, 51–69. MR 707348, DOI 10.1007/BF01393825
Chong-Kyu Han, Regularity and uniqueness of certain systems of functions annihilated by a formally integrable system of vector fields, Rocky Mountain J. Math. 18 (1988), no. 4, 767–783. MR 1002174, DOI 10.1216/RMJ-1988-18-4-767
Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886, DOI 10.1007/978-3-642-61981-6
Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
S. M. Webster, Analytic discs and the regularity of C-R mappings of real submanifolds in $\textbf {C}^{n}$, Complex analysis of several variables (Madison, Wis., 1982) Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc., Providence, RI, 1984, pp. 199–208. MR 740883, DOI 10.1090/pspum/041/740883
Robert B. Gardner, Differential geometric methods interfacing control theory, Differential geometric control theory (Houghton, Mich., 1982) Progr. Math., vol. 27, Birkhäuser, Boston, Mass., 1983, pp. 117–180. MR 708501
Peter J. Olver, Applications of Lie groups to differential equations, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1986. MR 836734, DOI 10.1007/978-1-4684-0274-2