C-l-contact and C-l-right equivalences of real semi-quasihomogeneous C-l function germs

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Data

2014-07-01

Autores

Carlos Ferreira Costa, Joao [UNESP]
Jose Sala, Marcelo
Humberto Soares Junior, Carlos

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Hiroshima Univ, Grad Sch Sci

Resumo

In this paper we investigate the C-l versions of contact and right equivalences of real semi-quasihomogeneous C-l function germs, 1 <= l <= infinity. The C-l-right equivalence implies C-l-contact equivalence for any 1 <= l <= infinity and in this work we show, up to certain conditions, that for semi-quasihomogeneous C-l function germs the converse is also true (Theorem 1). As a consequence, concerning the particular case of quasihomogeneous C-l function germs, we also have a similar result (Corollary 1) which recover a known result of M. Takahashi [14] for l = infinity. We note that we are considering semi-quasihomogeneous function germs with no additional hypothesis of isolated singularity at zero.

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contact equivalence, right equivalence, semi-quasihomogeneous germs

Como citar

Hiroshima Mathematical Journal. Higashi: Hiroshima Univ, Grad Sch Sci, v. 44, n. 2, p. 127-137, 2014.