Linear or circular move in space-time?

[pogono]

Hello all,
I would like to ask about such thing:

As we know, space is curved and limited, so moving in one direction with constant velocity we should come back to the same place that we begun (except that space is expanding, so it probably won't happen).

Can we then mathematically add "next dimension" and consider such move in space as circular with some conductive radius R placed in this new dimension?

If the answer is "Yes", so does it mean, that every linear move may be explained as some rotation?

Thank you for your response.

[Shaula]

3D and higher spaces can be intrinsically and extrinsically curved. One requires a higher dimension to curve into, one does not. So the answer is no, geodesics being closed does not necessarily equate to a rotation in higher dimensional space.

Plus the scenario you describe is in the simplest possible case for a finite, unbounded universe - there are other possibilities for the topology of spacetime. Spherical is just one option. So the bit beginning "As we know" - well, we don't really know. It is an option. More data is required.

[astromark]

So on reading this... My understanding is as yours.. my silly questions are not so odd at all..

My faith in my own ability to question and enquire is sound.. you ask the same as do I.. You have said it better..

[pogono]

Thank you, Shaula.
Thank you astromark.

I have some boring lectures at my PhD course so I suppose I will post some fresh ATM thread soon :-)
My new idea is related to my above question.