Geometry of D_4 conformal triality and singularities of tangent surfaces

DOI HANDLE Open Access

Abstract

It is well known that the projective duality can be understood in the context of geometry of An-type. In this paper, as D4-geometry, we construct explicitly a flag manifold, its triplefibration and differential systems which have D4-symmetry and conformal triality. Then we give the generic classification for singularities of the tangent surfaces to associated integral curves, which exhibits the triality. The classification is performed in terms of the classical theory on root systems combined with the singularity theory of mappings. The relations of D4-geometry with G2-geometry and B3-geometry are mentioned. The motivation of the tangent surface construction in D4-geometry is provided.

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Details

  • CRID
    1390572174748887808
  • NII Article ID
    120006459740
  • DOI
    10.14943/84195
  • HANDLE
    2115/69855
  • Text Lang
    en
  • Data Source
    • JaLC
    • IRDB
    • CiNii Articles
  • Abstract License Flag
    Allowed

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