Even dimensional improper affine spheres

Autor(es)

Craizer, Marcos ^[1] ; Domitrz, Wojciech ^[2] ; Rios, Pedro de M. ^[3]

Afiliação do(s) autor(es)

^[1] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, Rio de Janeiro, RJ - Brazil

^[2] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw - Poland

^[3] Univ Sao Paulo, Dept Matemat, ICMC, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 421, n. 2, p. 1803-1826, JAN 15 2015.
• Citações Web of Science: 3

Resumo

There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dimensions: the former class corresponds to the center-chord transform of a pair of Lagrangian submanifolds while the latter is related to special Kahler manifolds. Furthermore, we show that the improper affine spheres obtained in this way are solutions of certain exterior differential systems. Finally, we also discuss the problem of realization of simple stable Legendrian singularities as singularities of these improper affine spheres. (c) 2014 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/04630-9 - Geometria simplética e sistemas quânticos: questões em correspondências de símbolos
• Beneficiário: Pedro Paulo de Magalhaes Rios
• Modalidade de apoio: Bolsas no Exterior - Pesquisa