岑燕斌.Morse引理的一个推广[J].数学研究及应用,2000,20(2):287~290 |
Morse引理的一个推广 |
A Generalization of Morse Lemma |
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DOI:10.3770/j.issn:1000-341X.2000.02.028 |
中文关键词: C∞函数芽 同构 三阶Hessain 四阶Hessain. |
英文关键词:C∞ function germs isomorphic cubic Hessain Hessain of degree 4. |
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中文摘要: |
设En是在0∈Rn的C∞函数芽环,M是En中唯一的极大理想.如果f∈M2且其二阶Hessain是非退化的,则f同构于它的二阶Hessain,这就是著名的Morse引理.本文将讨论两个变元的C∞函数芽,得到:(1)若f∈M3?Exy,且其三阶Hessain是非退化的,则f同构于它的三阶Hessain.(2)若f∈M4?Exy |
英文摘要: |
Assume that En is the ring of the C∞ function germs at 0∈ Rn,M is the unique maximal ideal in En. If f ∈M2 and its quadratic Hessain is non-degenerate, then f is isomorphic to its quadratic Hessain. This is famous Morse lemma. In this paper, We will discuss C funtion germs in two variables. The results show that (1) If f∈M3?Exy and its cubic Hessain is non-degenerate, then f is isomorphic to its cubic Hessain. (2) If f∈M4?Exy and its Hessain of degree 4 is non-degenerate,then f is isomorphic to its Hessain of degree 4.Obviously, this is a generalization of Morse lemma. |
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