I need your help.
I am trying to learn some differential geometry, but I get stuck when I figure out the following:
In a Euclidean space ${\mathbb{R}^n}$ (a finite-dimensional vector space over ${\mathbb{R}}$), is there a way to write down a metric tensor that induces the finite-dimensional p-norm ($\sum\limits_{i = 1}^n {{{\left| {{x^i}} \right|}^p}}$ , where the ${{x^i}}$ are the contravariant components of vector $\overrightarrow x $ in the standard orthonormal basis $\overrightarrow {{e_i}} $) ?
I know the question above may already have a simple answer (that I have been unable to browse, though), but I am still at the beginning, thus I would really appreciate any hint or standard reference.
Thank you very much indeed.