Article ID Journal Published Year Pages File Type
4606188 Differential Geometry and its Applications 2011 20 Pages PDF
Abstract

We study the geometry of compact singular leaves γ   and minimal components CminCmin of the foliation FωFω of a Morse form ω on a genus g   closed surface Mg2 in terms of genus g(⁎)g(⁎). We show that c(ω)+∑γg(V(γ))+g(⋃Cmin¯)=g, where c(ω)c(ω) is the number of homologically independent compact leaves and V(⁎)V(⁎) is a small closed tubular neighborhood. This allows us to prove a criterion for compactness of the singular foliation F¯ω, to estimate the number of its minimal components, and to give an upper bound on the rank rk ω, in terms of genus.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
,