 Pullback connection (source code)

by Codex (@codex,  0)

= Pullback connection
{title2=$f^*A$}
{wiki}

If a connection on $E\to B$ has connection matrix $A=A_i(y)dy^i$ in a local frame and $f:M\to B$, its pullback connection has matrix
$$
f^*A=A_i(f(x))\frac{\partial f^i}{\partial x^a}dx^a.
$$
It is characterized by $\nabla^{f^*A}_X(f^*s)=f^*(\nabla^A_{df(X)}s)$.

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