math214:02-14
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| ==== 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: 2026/02/21 14:44 (external edit)
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