Geodesic
The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 455-466 
E. R. Avakov; A. A. Agrachev; A. V. Arutyunov. The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 455-466. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The level set $M$ of a smooth mapping $F$ in a neighborhood of an anormal point is investigated. Concepts of 2-regularity are introduced for it. It is proved that if the mapping is 2-regular at the point under consideration, then in a neighborhood of it the set $M$ is locally diffeomorphic to the set of zeros of the second differential of $F$.

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