I Is a Manifold with a Boundary Considered a True Manifold?

[jbergman]

About 2. I take it as, even though the metric tensor did not change along the induced flow of the vector field, a non-zero Lie Derivative would imply that the induced flow moves points in a neighborhood such that the 'distance' between them changes when 'flowed' by the same increase of the integral curves parameter.

In both cases that is true. But the distance can change because they have moved in a direction where the metric naturally changes like in the radial direction with the Schwarzschild metric. Or with a constant metric we move points differing distances under the same increase of the parameter.

Of course you can also have both.

 

[cianfa72]

Or with a constant metric we move points differing distances under the same increase of the parameter.

Constant in the sense that it does not change along the integral curves of the vector field, not necessarily that it must stay constant at each point in the manifold.

 

[sysprog]

I'm not sure I understand this comment. Are you talking about Minkowski space?

I was merely quibbling about the terms.