Even Dimensional Improper Affine Spheres

Autor:	Craizer, Marcos, Domitrz, Wojciech, Rios, Pedro de M.
Rok vydání:	2012
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Symplectic Geometry 53A15 53D12
Zdroj:	Journal of Mathematical Analysis and Applications 421 (2015) 1803-1826
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jmaa.2014.08.028
Popis:	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 K\"ahler 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. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1212.4722 Zobrazit plný text záznamu View this record from Arxiv