| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw - Poland
[2] Univ Sao Paulo, Dept Matemat, ICMC, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Geometriae Dedicata; v. 169, n. 1, p. 361-382, APR 2014. |
| Web of Science Citations: | 5 |
| Abstract | |
We study the global centre symmetry set (GCS) of a smooth closed submanifold . The GCS includes both the centre symmetry set defined by Janeczko (Geometria Dedicata 60:9-16, 1996) and the Wigner caustic defined by Berry (Philos Trans R Soc Lond A 287:237-271, 1977). The definition of GCS uses the concept of an affine -equidistant of . When is a Lagrangian submanifold in the affine symplectic space , we present generating families for singularities of and prove that the caustic of any simple stable Lagrangian singularity in a -dimensional Lagrangian fibre bundle is realizable as the germ of an affine equidistant of some . We characterize the criminant part of GCS in terms of bitangent hyperplanes to . Then, after presenting the appropriate equivalence relation to be used in this Lagrangian case, we classify the affine-Lagrangian stable singularities of GCS . In particular we show that, already for a smooth closed convex curve , many singularities of GCS which are affine stable are not affine-Lagrangian stable. (AU) | |
| FAPESP's process: | 10/15179-8 - Symplectic geometry applied to mathematical physics |
| Grantee: | Pedro Paulo de Magalhaes Rios |
| Support Opportunities: | Regular Research Grants |