Geodesic
Connection of Lagrangian singularities with Legendrian singularities under stereographic projection
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 533-540 
V. D. Sedykh. Connection of Lagrangian singularities with Legendrian singularities under stereographic projection. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 533-540. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a14/
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     author = {V. D. Sedykh},
     title = {Connection of {Lagrangian} singularities with {Legendrian} singularities under stereographic projection},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_2_a14/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the evolute of a smooth closed submanifold in general position in a Euclidean space has the same number of isolated singularities of each simple class as has the front of its stereographic image in a space of 1 higher dimension.

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