Equivalence of real Milnor fibrations for quasi-homogeneous singularities

Abstract

We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement of "link" in sphere are equivalents, since they exist. Moreover, in order to do that, we explicitly characterize the critical points of projection $\frac{f}{\|f\|}:S_{\epsilon}^{m}\setminus K_{\epsilon}\to S^{1}$, where $K_{\epsilon}$ is the link of singularity.