Global solvability of systems on compact surfaces

Author(s)

Giuliano Angelo Zugliani

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2014-07-25

Examining board members

Adalberto Panobianco Bergamasco; Paulo Domingos Cordaro; Jorge Guillermo Hounie; Paulo Leandro Dattori da Silva

• Advisor: Adalberto Panobianco Bergamasco; Alberto Parmeggiani; Sergio Luis Zani

Abstract

We are interested in studying an involutive system defined by a closed non-exact 1-form on a closed and orientable surface. Here we present a necessary condition for the global solvability of this system. We also make some particular constructions of globally solvable systems that motivate the equivalence between the global solvability and the necessary condition, for two cases involving 1-forms of the Morse type, namely, when the surface is the bitorus or when the 1-form is generic (AU)