Terminology for "coordinates"

Question

As a non-native speaker, I am not sure about the following terminology for coordinates on manifolds.

Given a manifold $M$, we pick up a local coordinates $(U, x^i)$, where $x^i$ are functions on $U$.

Now give a $\mathbb{R}$-valued function $f$ on $U$, we can expand it as Taylor series $$ f=\sum f_I x^I, \quad I=\{i_1,i_2,\dots\} $$ what is the English term for $f_I$? I call it component, but my professor (a non-native speaker too) argues that it is wrong.

1

"Taylor coefficients"? – Qiaochu Yuan May 05 '14 at 17:06

score 2 · Answer 1 · answered May 05 '14 at 23:35

2

I would say "coefficients relative to the local coordinate system", or just "coefficients" for short.

answered May 05 '14 at 23:35

mweiss

23,647

Terminology for "coordinates"

1 Answers1