Cl-contact and Cl-right equivalences of real semi-quasihomogeneous Cl function germs

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Costa, Joaõ Carlos Ferreira [UNESP]
Saia, Marcelo José
Soares Júnior, Carlos Humberto
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In this paper we investigate the Cl versions of contact and right equivalences of real semi-quasihomogeneous Cl function germs, 1 ≤ l ≤ ∞. The Cl-right equivalence implies Cl-contact equivalence for any 1≤ l ≤ ∞ and in this work we show, up to certain conditions, that for semi-quasihomogeneous Cl function germs the converse is also true (Theorem 1). As a consequence, concerning the particular case of quasihomogeneous Cl function germs, we also have a similar result (Corollary 1) which recover a known result of M. Takahashi [14] for l=∞. We note that we are considering semi-quasihomogeneous function germs with no additional hypothesis of isolated singularity at zero.
Contact equivalence, Right equivalence, Semi-quasihomogeneous germs
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Hiroshima Mathematical Journal, v. 44, n. 2, p. 127-137, 2014.