Video10-TA09: metric tensor/calculating distances/raising and lowering indices

[@ritwikbandyopadhyay2376]

Thank you, your explanations are very clear

[@evanr.lowetechgamingandcoo1410]

Great thanks.

[@theillusionzone]

Great video, I only have one question at 35:28 where did that equality come from? X^i e_i=X_i e^i?

[@physl2787]

Which books should i Use to understand this stuff.

[@konstantinparchevsky2031]

If lowering index 35:26 X_i = g_{ij} X^j (1) is valid for any vector, then it should be correct for dX_i vector as well dX_i = g_{ij} dX^j (2) On the other hand, taking differential from both sides of Eq.(1) gives us expression containing derivatives from g_{ij} (because, in general, g_{ij} depends on the coordinates). This expression will not coincide with Eq.(2). Q. If I need to lower/raise index in dX_i or dX^i, how can I do this?

[@AbhishekSachans]

At 38:04, I see you don't write 'm' just below alpha. Why is that so? Why do we need to retain the 'old' position of the index? Please explain.

[@dermotgreen-queensuniversi7504]

... in some cases it helps to retain the original position (for ease of understanding, or if you know what the index refers to specifically).

[@AbhishekSachans]

@@dermotgreen-queensuniversi7504 Hmm I get it. Thank you for the answer Mr. Green.

[@lukmaes6290]

I m too old for this !