Skip to main content
4 votes

Confusion on Notations of Partial Derivatives on Manifolds

See this answer of mine for a direct answer. What follows is just some personal remarks. I actually don’t quite like the way Tu presents the definition. Definitions. Definition 1. (Partial derivative ...
peek-a-boo's user avatar
  • 58.4k
1 vote
Accepted

Change of coordinates in a regular surface $S$.

Call $C=X^{-1}\circ Y$, then $Y=X\circ C$ and the derivatives are connected as $$JY_p=JX_{C(p)}\ JC_p,$$ by the chain's rule. Using the canonical basis you can get $$JY_pe_1=JX_{C(p)}\ JC_pe_1,$$ and ...
janmarqz's user avatar
  • 10.6k

Only top scored, non community-wiki answers of a minimum length are eligible