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Examples in the theory of sufficiency of jets. (English) Zbl 0594.58008
Summary: It is shown that for a given nonnegative integer s, there exist a positive integer r(s) and an r(s)-jet \(v_ s\) with source at \(O\in {\mathbb{R}}^ 3\) which is not V-sufficient in the class of \(C^{r(s)+s}\)- realizations and is \(C^ 0\)-sufficient in the class of \(C^{r(s)+s+1}\)- realizations. In the complex case, a jet with source at \(O\in {\mathbb{C}}^ 2\) which is V-sufficient but not \(C^ 0\)-sufficient in the class of holomorphic realizations is constructed.

58A20 Jets in global analysis
57R45 Singularities of differentiable mappings in differential topology
Full Text: DOI
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