Geodesic
Configurations of an Articulated Arm and Singularities of Special Multi-Flags
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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P. Mormul has classified the singularities of special multi-flags in terms of “EKR class” encoded by sequences $j_1,\dots, j_k$ of integers (see [Singularity Theory Seminar, Warsaw University of Technology, Vol. 8, 2003, 87–100] and [Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157–178]). However, A.L. Castro and R. Montgomery have proposed in [Israel J. Math. 192 (2012), 381–427] a codification of singularities of multi-flags by RC and RVT codes. The main results of this paper describe a decomposition of each “EKR” set of depth $1$ in terms of RVT codes as well as characterize such a set in terms of configurations of an articulated arm. Indeed, an analogue description for some “EKR” sets of depth $2$ is provided. All these results give rise to a complete characterization of all “EKR” sets for $1\leq k\leq 4$.
Keywords: special multi-flags distributions; Cartan prolongation; spherical prolongation; articulated arm; rigid bar. 
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     title = {Configurations of an {Articulated} {Arm} and {Singularities} of {Special} {Multi-Flags}},
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Fernand Pelletier; Mayada Slayman. Configurations of an Articulated Arm and Singularities of Special Multi-Flags. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a58/

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