Connection of Lagrangian singularities with Legendrian singularities under stereographic projection
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 533-540
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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.
@article{SM_1995_83_2_a14,
author = {V. D. Sedykh},
title = {Connection of {Lagrangian} singularities with {Legendrian} singularities under stereographic projection},
journal = {Sbornik. Mathematics},
pages = {533--540},
year = {1995},
volume = {83},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1995_83_2_a14/}
}
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/
[1] Sedykh V. D., “Teorema o chetyrekh vershinakh vypukloi prostranstvennoi krivoi”, Funktsion. analiz i ego pril., 26:1 (1992), 35–41 | MR | Zbl
[2] Kneser A., “Bemerkungen uber die Anzahl der Extreme der Krummung geschlossenen Kurven und uber verwandte Fragen in einer nicht-euklidischen Geometrie”, Festschrift, 70, Geburstag von H. Weber, Leipzig, 1912, 170–192
[3] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, T. 1, Nauka, M., 1982 | MR
[4] Feldman E. A., “On parabolic and umbilic points of immersed hypersurfaces”, Trans. Amer. Math. Soc., 127 (1967), 1–28 | DOI | MR | Zbl