open access

https://doi.org/10.14943/84195

https://hdl.handle.net/2115/69855

Geometry of D_4 conformal triality and singularities of tangent surfaces

英語

2014-03-25

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

1051

1-17

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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