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Question: covariant derivative in spherical coordinates

Question:covariant derivative in spherical coordinates

Indah Huegele 20 Maple 18
September 05 2014
3

I have been learning to use the Physics package in Maple 18.  I just updated to the latest version of the Physics package to see if it would fix the problem by my results are the same.

When I take a covariant derivative in spherical coordinates it does not appear to have a scale factor such as g_kk below.  

A_(j;k)=1/(g_(kk))(partialA_j)/(partialx_k)-Gamma_(jk)^iA_i,

This definition of comes from the Mathworld web site.  I think they have a typo such that it should actually read h_k which is the scale factor instead of g_kk which is the metric.  They are related by h_k^2 = g_kk.

Why doesn't Maple's covariant derivative have the scale factor when I am differentiating in spherical coordinates?

Thanks!
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