Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

As per the title, I'm just looking for a reference with a convenient derivation (or at minimum, description) of the Euclidean metric in hyperspherical coordinates. The specific cases of polar or 3-dimensional spherical coordinates are not helpful.

share|improve this question

1 Answer 1

up vote 3 down vote accepted

I don't know about a reference, but I can show you how to construct it inductively. We have $$g_{Euc} = dr^2 + r^2g_{S^{n-1}},$$ where $g_{S^{n-1}}$ is the round metric on the $n-1$ sphere. So it remains to construct $g_{S^n}$ inductively. Well, $$g_{S^n} = d\rho^2 + \sin^2(\rho)g_{S^{n-1}}.$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.