Geodesic
On singularities of folding type
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1119-1134

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In this article we find necessary and sufficient conditions for the existence of a mapping with a singularity of folding type on a given submanifold. 
@article{IM2_1970_4_5_a6,
     author = {Ya. M. Eliashberg},
     title = {On singularities of folding type},
     journal = {Izvestiya. Mathematics },
     pages = {1119--1134},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a6/}
}
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Ya. M. Eliashberg. On singularities of folding type. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1119-1134. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a6/