A Generalization of Morse Lemma
  
Key Words: C function germs   isomorphic   cubic Hessain   Hessain of degree 4.  
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Author NameAffiliation
CEN Yan-bin Dept. of Math.
Qiannan Teachers′ College
Duyun 558000 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2000.02.028
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