# Changes

## Linear connection

, 17:29, 6 January 2012
no edit summary
===Definition part (pointwise form)===
A '''linear connection''' is a smooth choice $\nabla$ of the following: at each point $p \in M$, there is a map ${}^p\nabla: T_p(M) \times \Gamma(TM) \to T_p(M)$, satisfying some conditions. The map is written as ${}^p\nabla_X(v)$ where $X \in T_p(M)$ and $v \in \Gamma(ETM)$.
* It is $\R$-linear in $X$ (that is, in the $T_p(M)$ coordinate).
* It is $\R$-linear in $\Gamma(TM)$ (viz the space of sections on $ETM$).
* It satisfies the following relation called the Leibniz rule: