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Range of divergence operator on the space of traceless symmetric $(0,2)$ tensors; conformal vector fields on an arbitrary metric on $S^2$
Let $\gamma$ be a metric on $S^2$.
I am trying to solve the following PDE on a $(0,2)$ symmetric traceless tensor $A$:
$$div_{\gamma} A = \omega$$
where $\omega$ is a 1-form.
It is known that there ...
- 969
4
votes
1
answer
685
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Horizontal lift of differential operator
On a Riemannian manifold $M$, there is a canonical horizontal lift $X^{\mathrm{hor}}$ of vector fields $X$ to $TM$, which is characterized by the two properties that
$X^{\mathrm{hor}}$ is a ...
- 9,853