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Hello, I have a question regarding the first equation above.

it says du^{i}=a^{i}*dr=a^{i}*a^{j}*du_{j}but I wonder how. (sorry I omitted vector notation because I don't know how to put them on)

if du^{i}=a^{i}*dr=a^{i}*a^{j}*du_{j}is true, then

dr=a^{j}*du_{j}

|dr|*r^{hat}=|a^{j}|*du_{j}*a^{j}^{hat}

where lim |dr|,|du_{j}|->0

which means r^{hat}=a^{j}^{hat}.

are both the directions actually the same or do we just don't care about directions because both will eventually be small increment of each component?

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# I Metric tensor derivation

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