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초록· 키워드
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Given a system of smooth 1-forms θ = (θ^1,…,θ^s) on a
smooth manifold Mm, we give a necessary and sufficient condition for M
to be foliated by integral manifolds of dimension n, n ≤ p := m −s, and
construct an integrable supersystem (θ,η) by finding additional 1-forms
η = (η^1, . . . , η^(p−n)). We also give a necessary and sufficient condition for
M to be foliated by reduced submanifolds of dimension n, n ¸ p, and construct
an integrable subsystem (dρ^1, . . . , dρ^(m−n)) by finding a system of
first integrals ρ = (ρ^1, . . . , dρ^(m−n)). The special case n = p is the Frobenius
theorem on involutivity.
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참고문헌 (15)
참고문헌 신청
A. Clebsch / 1866 / ¨ Uber die simultane Integration linearer partieller Differentialgleichungen / J. Reine Angew. Math. 65 : 257 ~ 268
C. K. Han / / Complex submanifolds in real hypersurfaces / preprint
C. K. Han / / Integrable submanifolds in almost complex submanifolds / preprint
C. K. Han / 2008 / Pfaffian systems of Frobenius type and solvability of generic overdetermined PDE systems, Symmetries and overdetermined systems of partial differential equ
E. A. Coddington / 1955 / Theory of Ordinary Differential Equations / McGraw-Hill
C. K. Han / / Complex submanifolds in real hypersurfaces / preprint
C. K. Han / / Integrable submanifolds in almost complex submanifolds / preprint
C. K. Han / 2008 / Pfaffian systems of Frobenius type and solvability of generic overdetermined PDE systems, Symmetries and overdetermined systems of partial differential equ
E. A. Coddington / 1955 / Theory of Ordinary Differential Equations / McGraw-Hill
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