Title of article :
Singularities of improper affine maps and their Hessian equation
Author/Authors :
Milلn، نويسنده , , Francisco، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2013
Abstract :
We study improper affine spheres with some admissible singularities, called improper affine maps, and associated to the unimodular Hessian equation. In particular, we characterize when a curve of R 3 is the singular curve of some improper affine map with prescribed cuspidal edges and swallowtails. Also, we consider improper affine maps with isolated singularities and show some similarities and differences between the Hessian +1 equation and the Hessian −1 equation. As a consequence, we construct global examples with the desired singularities.
Keywords :
Cuspidal edges , Improper affine spheres , Swallowtails , Isolated singularities , Unimodular Hessian equation
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications