1
$\begingroup$

Let $M$ be a real manifold and let $\{(U_\alpha,\phi_{\alpha})\}_{\alpha\in I}$ $\{(V_\beta,\psi_\beta)\}_{\beta\in J}$ be two oriented atlases. Let's define, for $p\in U_\alpha\cap V_\beta$, $\alpha\in I$, $\beta \in J$ $$ v(p):=\frac{|J(\phi_\alpha\circ\psi^{-1}_\beta)_{\psi_\beta(p)}|}{J(\phi_\alpha\circ\psi^{-1}_\beta)_{\psi_\beta(p)}} $$ I have to notice that $v$ is a smooth function...

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.