Índice de n-formas diferenciáveis totalmente reais

• Autor(a) principal: Oliveira, Isabelly Camila Diniz de
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9245
• topic: n-Forma diferencial totalmente real; Índice; Folheações; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we studied totally real di erential n-forms in a neighborhood of an isolated singular point. Using the geometric approach, we study a de nition of index for this equations classes, which coincides with the classic de nition of Hopf to the index of positive quadratic di erential equations, and these index is invariant for di eomorphisms that preserve totally real di erential n-forms. We also show a generalization of the Poincar e-Hopf theorem for the index of a totally real di erential n-forms. Moreover, using complex coordinates we obtain a formula for the index in terms of the coe cients of the totally real di erential n-form. Lastly, we use the polar blow-up method to study totally real di erential n-forms with non degenerate principal part. We also obtained a generalization of the Bendixon formula.