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Global stability of special multi-flags

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Abstract

In this paper, we study special multi-flags on manifolds. A special multiflag is a certain nested sequence of subbundles of the tangent bundle which are derived by Lie brackets. A property of a special multi-flag is characterized by the existence of a completely integrable subdistribution of corank one in the largest distribution in the sequence, which is a so-called covariant subdistribution. It is proved that a one-parameter deformation of a special multi-flag on a compact manifold can be described by a family of global diffeomorphisms of the underlying manifold, if the covariant subdistribution of the largest distribution in the flag is preserved.

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Authors and Affiliations

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

    Jiro Adachi

  2. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Jiro Adachi

Authors
  1. Jiro Adachi
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Correspondence to Jiro Adachi.

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partially supported by 21st Century COE Programs “Mathematics of Nonlinear Structure via Singularity”, “Topological Science and Technology”, Hokkaido University, and Grants-in-Aid for Young Scientists (B), No. 17740027, Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Adachi, J. Global stability of special multi-flags. Isr. J. Math. 179, 29–56 (2010). https://doi.org/10.1007/s11856-010-0072-3

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  • DOI: https://doi.org/10.1007/s11856-010-0072-3

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