Intrinsic Lipschitz Sections of no-linear Quotient Maps

Le Donne and the author introduced the so-called intrinsically Lipschitz sections of a fixed quotient map π in the context of metric spaces. Moreover, the author introduced the concept of intrinsic Cheeger energy when the quotient map is also linear. In this note we investigate about the no-linearity of π. In particular, we find a Leibniz formula for the intrinsic slope when π satisfies a weaker condition. After that, we focus our attention on Carnot groups and using the properties of intrinsic dilations we show that the dilation of a Lipschitz section is so too.