THE NUMBER OF MINIMAL COMPONENTS AND HOMOLOGICALLY INDEPENDENT COMPACT LEAVES OF A WEAKLY GENERIC MORSE FORM ON A CLOSED SURFACE

I. GELBUKH

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THE NUMBER OF MINIMAL COMPONENTS AND HOMOLOGICALLY INDEPENDENT COMPACT LEAVES OF A WEAKLY GENERIC MORSE FORM ON A CLOSED SURFACE

机译：闭合表面上弱一般莫氏形式的最小成分数和在同性学上独立的紧密叶

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On a closed orientable surface M_g~2 of genus g, we consider the foliation of a weakly generic Morse form ω on M_g~2 and show that for such forms c(ω) + m(ω) = g ? (1/2)k(ω), where c(ω) is the number of homologically independent compact leaves of the foliation, m(ω) is the number of its minimal components, and k(ω) is the total number of singularities of ω that are surrounded by a minimal component. We also give lower bounds on m(ω) in terms of k(ω) and the form rank rk ω or the structure of ker [ω], where [ω] is the integration map.

机译：在属g的闭合可定向曲面M_g〜2上，我们考虑了M_g〜2上弱通用莫尔斯形式ω的叶状，并证明对于这种形式c（ω）+ m（ω）= g？（1/2）k（ω），其中c（ω）是同叶的同源独立紧凑叶的数量，m（ω）是其最小成分的数量，k（ω）是奇点总数被最小分量包围的ω我们还根据k（ω）和形式rkω或ker [ω]的结构给出m（ω）的下界，其中[ω]是积分图。

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《The Rocky Mountain journal of mathematics》 |2013年第5期|共16页
作者
I. GELBUKH;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Surface; Morse form foliation; number of minimal components;

机译：表面;莫尔斯形叶状;最少成分数;

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1. THE NUMBER OF MINIMAL COMPONENTS AND HOMOLOGICALLY INDEPENDENT COMPACT LEAVES OF A WEAKLY GENERIC MORSE FORM ON A CLOSED SURFACE [J] . I. GELBUKH The Rocky Mountain journal of mathematics . 2013,第5期

机译：闭合表面上弱一般莫氏形式的最小成分数和在同性学上独立的紧密叶
2. The Morse theory of two-dimensional closed branched minimal surfaces and their generic non-degeneracy in Riemannian manifolds [J] . A. J. Tromba Calculus of variations and partial differential equations . 2000,第2期

机译：黎曼流形中二维封闭分支最小曲面的莫尔斯理论及其一般非简并性
3. Close cohomologous Morse forms with compact leaves [J] . Gelbukh I. Czechoslovak Mathematical Journal . 2013,第2期

机译：紧密的同源摩尔斯形式，叶片紧密
4. The closed-form frequency-independent solution for physical optics integrals on conducting quadratic surfaces using rectangular meshing [C] . Koushyar Farzad Mokhtari, Shishegar Amir Ahmad International Symposium on Telecommunications . 2014

机译：使用矩形网格划分传导二次曲面上物理光学积分的闭式频率独立解
5. Closed minimal hypersurfaces in compact symmetric spaces. [D] . Gorodski, Claudio. 1992

机译：在紧凑的对称空间中封闭的最小超曲面。
6. Minimal Surfaces Spanning Closed Manifolds [O] . R. Courant, N. Davids 1940

机译：最小的曲面跨越封闭的流形
7. Number of minimal components and homologically independent compact leaves for a Morse form foliation [O] . Irina Gelbukh, Communicated A. Némethi 2012

机译：莫尔斯电离叶形的最小成分数和同源独立的紧密叶的数量

THE NUMBER OF MINIMAL COMPONENTS AND HOMOLOGICALLY INDEPENDENT COMPACT LEAVES OF A WEAKLY GENERIC MORSE FORM ON A CLOSED SURFACE

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