cianfa72's latest activity

Ok, indeed. My point was to stress the notion of parallel and FW transport: assign a curve C, a point P on it and a vector V at P (i.e...

So, FW transport along any curve will preserve all of these properties. Parallel transport will only preserve them along a geodesic. For...

Yes, of course. I'm not asking about specific properties of frame field. I'm asking about the simple case of FW transport of a set of...

No. Given any curve C, a point P on it and a vector V at P one can solve the first-order differential equation for the parallel...

Ah ok, maybe I wasn't very clear in post #22. In the general case (not geodesic curve) for both parallel and FW transport we need to...

I think the same is true for parallel transport since it is defined for any curve including non-geodesic ones. However I never said...

But that operation is typically called the exponential map (and is a completely rigorous construct)...

Ok yes. Yes, however the curve C is known (it is the observer's worldline) hence the tangent vector ##\mathbf u## along the curve...

I'm not sure whether the following argument applies to FW transport as well. Take the parallel transport equation along a curve C from...

Yes. That's the only orthogonality condition we've discussed.

A set of points forming a one-dimensional curve. But that's because you specified the orthogonality condition. If you don't specify the...

Note that this "exponentiation" operation isn't really well-defined, rigorously speaking, because it treats tangent vectors as...

As long as it's a sufficiently small length compared with the scale of the spacetime curvature.

Moderator's note: Spin-off from another thread due to topic change. In the second link referenced, there is a claim about a physical...

In the category of topological spaces and homeomorphisms, one can define those manifolds which are made from gluing two disks along...