otaniyul
Jan5-10, 06:39 PM
Hello, fellows! Can someone help me?
Is there a difference between densities and n-forms in a manifold? Bar's "Wave equations on Lorentzian Manifolds" states that densities are linear funcions of n-forms onto the real numbers,
| \Lambda M | : \Lambda^n T^*M \to \Re
If that is the case, then given a map f : M \to N between manifolds, f induces a pullback between n-forms, but pushfoward between densities. Is that correct? I've heard somewhere that when no problem of orientation arises, n-forms and densities can be identified, but it seems not to be the case here... and somewhere else in the book, I think Bar uses a pullback in densities... please help...
Is there a difference between densities and n-forms in a manifold? Bar's "Wave equations on Lorentzian Manifolds" states that densities are linear funcions of n-forms onto the real numbers,
| \Lambda M | : \Lambda^n T^*M \to \Re
If that is the case, then given a map f : M \to N between manifolds, f induces a pullback between n-forms, but pushfoward between densities. Is that correct? I've heard somewhere that when no problem of orientation arises, n-forms and densities can be identified, but it seems not to be the case here... and somewhere else in the book, I think Bar uses a pullback in densities... please help...