In Euclidean space, we may define covariant basis by the partial derivative of position vector with respect to each coordinates, i.e.(adsbygoogle = window.adsbygoogle || []).push({});

##∂R/(∂z^i )=z_i##

But in curved space (such as, the two dimensional space on a sphere) how can we define covariant basis 'intrinsicly'?(as we have no position vector in curved space intrinsicly)

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# How to define covariant basis in curved space 'intrinsicly'?

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