Binary differential equations at parabolic and umbilical points for $2$-parameter families of surfaces

Autor:	Silva, Jorge Luiz Deolindo, Kabata, Yutaro, Ohmoto, Toru
Rok vydání:	2017
Předmět:	Mathematics - Differential Geometry Mathematics - Geometric Topology 53A20 37G10 34A09 58K05
Druh dokumentu:	Working Paper
Popis:	We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic $2$-parameter families of surfaces in $\mathbb P^3$ by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1708.04918 Zobrazit plný text záznamu View this record from Arxiv