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Geometry of Linear Differential Systems Towards Contact Geometry of Second Order

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Symmetries and Overdetermined Systems of Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 144))

Abstract

This is a lecture note on the geometry of linear differential systems. By a (linear) differential system (or Pfaffian system) (M, D), we mean a subbundle D of the tangent bundle T(M) of a manifold M. Locally D is defined by 1-forms w 1,...,w s such that w 1Λ⋯Λw s ≠0 at each point , where r is the rank of D and r + s = dim M;

$$ D = \{ \omega _1 = \cdots = \omega _s = 0\} . $$

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Keizo Yamaguchi

Authors
  1. Keizo Yamaguchi
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, The University of Adelaide, SA, 5005, Australia

    Michael Eastwood

  2. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN, 55455

    Willard Miller Jr.

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Yamaguchi, K. (2008). Geometry of Linear Differential Systems Towards Contact Geometry of Second Order. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_8

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