Journal of Prime Research in Mathematics

Milnor Fibrations and Regularity Conditions for Real Analytic Mappings

Khurram Shabbir\(^{a,*}\)

\(^a\)Department of Mathematics, Government College University, Katchery Road 54000, Lahore Pakistan.


Correspondence should be addressed to:


When ƒ: \((\mathbb{R^n},0)\)→\((\mathbb{R^p},0)\)is a surjective real analytic map with isolated critical value, we prove that the(m)-regularity condition (in a sense we define) ensures that \(\frac{f}{||f||}\) is a fibration on small spheres, ƒ induces afibration on the tubes and these fibrations are equivalent.In particular, we make the statement of [12] more precise in the case of an isolated critical point and weextend it to the case of an isolated critical value.


Milnor Fibrations, Analytic Mapping, Regularity, Submersion