Portuguese term for "path metric"

Question

Do anybody knows what is the usual translation to Portuguese for "path metric"?

(Given a metric space $(M,d)$, $d$ is called a "path metric" if, given any pair $(x,y)\in M\times M$, there exists a path $\gamma$ joining $x$ to $y$ with $d(x,y)=L(\gamma)$, where $L(\gamma)$ is the length of $\gamma$...)

With "usual translation" I mean the term that is often used to refer to the above definition. Of course I know that "path metric" means "métrica de caminhos", but I don't know if this is the usual term in Portuguese...

Answer 1

I think it should be métrica geodésica.