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FOLIATIONS ASSOCIATED WITH PFAFFIAN SYSTEMS
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 Title & Authors
FOLIATIONS ASSOCIATED WITH PFAFFIAN SYSTEMS
Han, Chong-Kyu;
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 Abstract
Given a system of smooth 1-forms = (,...,) on a smooth manifold , 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 () by finding additional 1-forms = (,...,). 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 (,...,) by finding a system of first integrals ,...,. The special case n = p is the Frobenius theorem on involutivity.
 Keywords
Pfaffian system;integral manifolds;reduced manifolds;foliation;Frobenius integrability;
 Language
English
 Cited by
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Local Geometry of Levi-Forms Associated with the Existence of Complex Submanifolds and the Minimality of Generic CR Manifolds, Journal of Geometric Analysis, 2012, 22, 2, 561  crossref(new windwow)
3.
Method of characteristics and first integrals for systems of quasi-linear partial differential equations of first order, Science China Mathematics, 2015, 58, 8, 1665  crossref(new windwow)
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A Frobenius theorem for corank-1 continuous distributions in dimensions two and three, International Journal of Mathematics, 2016, 27, 08, 1650061  crossref(new windwow)
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Invariant submanifolds for systems of vector fields of constant rank, Science China Mathematics, 2016, 59, 7, 1417  crossref(new windwow)
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