Curved Space-time and Relative Velocity

[Dale]

OK, now I am completely lost. Would you stop referring to posts which refer to other posts and simply post your question in one complete post. In post 325 you referred vaguely back to post 137 where you described two spaces:

1)I consider a "Semi-hemispherical spherical" bowl with a flat lower surface[I can have it by slicing a sphere at the 45 degree latitude].A vector is parallel transported along the circular boundary a little above the flat surface[or along the boundary of the flat surface as a second example] . The extent of reorientation of the vector seems to attribute similar characteristics of the surfaces on either side of the curve.How do we explain this?

2) We come to the typical example of moving a vector tangentially from along a meridian,from the equator to the north pole and then bringing it back to the equator along another meridian, by parallel transport and then back to the old point by parallel transporting the vector along the equator. It changes its direction . Now if we make the corners "smooth" it seems intuitively that the vector is not changing its orientation. Even if it changes its orientation it is not going to be by any large amount while the curvature of the included surface remains virtually the same. How does this happen?

Your semi-hemispherical bowl with a flat lower surface and the same space but with smooth corners.

If you are not talking about those two spaces then just be explicit with your complete question in one self-contained post where you describe the issue in detail without referring back to any previous posts.

 

[Anamitra]

2) We come to the typical example of moving a vector tangentially from along a meridian,from the equator to the north pole and then bringing it back to the equator along another meridian, by parallel transport and then back to the old point by parallel transporting the vector along the equator. It changes its direction . Now if we make the corners "smooth" it seems intuitively that the vector is not changing its orientation. Even if it changes its orientation it is not going to be by any large amount while the curvature of the included surface remains virtually the same. How does this happen?

Thread #327 clearly refers to the above quoted problem. My subsequent postings/replies are related to the above example.