Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

Autor(es)

Domitrz, Wojciech ^[1] ; Rios, Pedro de M. ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 169, n. 1, p. 361-382, APR 2014.
• Citações Web of Science: 5

Resumo

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)

• Processo FAPESP: 10/15179-8 - Geometria simplética aplicada a física matemática
• Beneficiário: Pedro Paulo de Magalhaes Rios
• Modalidade de apoio: Auxílio à Pesquisa - Regular