$D_{n}$-geometry and singularities of tangent surfaces (Theory of singularities of smooth mappings and around it)

Abstract

The geometric model for D_{n}-Dynkin diagram is explicitly constructed and associated generic singularities of tangent surfaces are classified up to local diffeomorphisms. We observe, as well as the triality in D_{4} case, the difference of the classification for D_{3}, D_{4}, D5 and D_{n}(ngeq 6), and a kind of stability of the classification in D_{n} for nrightarrow ∞. Also we present the classifications of singularities of tangent surfaces for the cases B_{3}, A3= D_{3}, G_{2}, C_{2} = B_{2} and A_{2} arising from D_{4} by the processes of foldings and removings.