Geometry of manifolds in the euclidian space and in the Minkowski space
Geometric analysis and variational problems in Riemannian and Kähler geometry
| Full text | |
| Author(s): |
Craizer, Marcos
;
Domitrz, Wojciech
;
Rios, Pedro de M.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ADVANCES IN MATHEMATICS; v. 374, p. 33-pg., 2020-11-18. |
| Abstract | |
Given a Lagrangian submanifold L of the affine symplectic 2n-space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension 2n, both of whose sets of singularities contain L. Although these improper affine spheres (IAS) always present other singularities away from L(the off-shell singularities studied in [8]), they may also present singularities other than Lwhich are arbitrarily close to L, the so called singularities "on shell". These on-shell singularities possess a hidden Z(2) symmetry that is absent from the off-shell singularities. In this paper, we study these canonical IAS obtained from Land their onshell singularities, in arbitrary even dimensions, and classify all stable Lagrangian/Legendrian singularities on shell that may occur for these IAS when Lis a curve or a Lagrangian surface. (C) 2020 The Authors. Published by Elsevier Inc. (AU) | |
| FAPESP's process: | 15/02029-1 - Symplectic geometry and the quantum-classical correspondence |
| Grantee: | Pedro Paulo de Magalhaes Rios |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/09249-0 - Affine geometry and Lagrangian-Legendrian singularities |
| Grantee: | Pedro Paulo de Magalhaes Rios |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |