cianfa72's latest activity

Ah ok, ##(1,2)## for instance is a smooth vector field that has constant components in coordinate basis ## \{\partial / \partial...

Sorry, not sure to understand which are the two your linearly independent vector fields ##(\omega_1,\omega_2)## and...

Yes. Better, I'd say since a smooth manifold is first and foremost a topological manifold, we can cover it iff, as topological manifold...

you can cover a manifold with a single chart if only this manifold is diffeomorphic to an open subset of ##\mathbb{R}^m##. I do not...

I'm a bit confused by the conditions on the existence of coordinate basis given by Frobenius's theorem. Namely, let's take a...

Ah yes, you're right (I edited my post #20). Coming back to what @Ibix said in post #10, I've not a clear understanding why a non...

For your first assumption, that's true. For your second assumption, that the topology allows for a global inertial chart, why do you...

On a second thought, I believe my post #19 isn't entirely correct. For a given spacetime, assume there exists a Lorentzian frame field...

Another point related to post #18. For a given spacetime suppose there is a set of 4 (algebraically) independent vector fields of...

When discussing isometric embeddings, there is a little more to it. The metric of the submanifold is taken to be induced from the...

As far as I can tell, by picking a pointwise non-orthogonal basis vector fields (one timelike and three spacelike) with constant...

Ok, so your "therefore" should not have been there.

Right, the latter is unrelated to the former. I just restated the conditions @Ibix put forward in post #10.

Ah yes. The definition of frame field/tetrad/vierbein requires pointwise mutual orthogonality of frame's vectors fields evaluated at any...

But your argument was you can’t embed a plane in e.g. a 3 sphere because the plane has zero curvature and the sectional curvature in...