math214:02-14
Differences
This shows you the differences between two versions of the page.
|
math214:02-14 [2020/02/14 09:06] pzhou created |
math214:02-14 [2020/02/19 01:27] (current) pzhou [Covector Fields (Differential 1-form)] |
||
|---|---|---|---|
| Line 40: | Line 40: | ||
| ==== Covector Fields (Differential 1-form) ==== | ==== Covector Fields (Differential 1-form) ==== | ||
| Recall how we define smooth vector field over $M$: it is an assignment $p \mapsto X(p) \in T_p M$ for $p \in M$, such that if we write it in coordinate patch $(U, (x_i))$, we have | Recall how we define smooth vector field over $M$: it is an assignment $p \mapsto X(p) \in T_p M$ for $p \in M$, such that if we write it in coordinate patch $(U, (x_i))$, we have | ||
| - | $$ X(p) = \sum_i X(p)^i \pa_i $$ | + | $$ X(p) = \sum_i X(p)^i \d_i $$ |
| where $X(p)^i:U \to \R$ are smooth functions. | where $X(p)^i:U \to \R$ are smooth functions. | ||
math214/02-14.1581699965.txt.gz · Last modified: 2020/02/14 09:06 by pzhou
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
