= Tensor density
A tensor density of weight $w$ transforms like a <tensor> with an additional factor $|\det(\partial x/\partial x')|^w$ under $x\mapsto x'$. A scalar density of weight one can be integrated against the coordinate volume element to give an invariant integral. On a spatial hypersurface, $\sqrt h$ is such a scalar density; hence $\pi^{ij}=\sqrt h p^{ij}$ is a tensor density when $p^{ij}$ is an ordinary tensor. The <Levi-Civita connection> extends to densities and satisfies $D_i\sqrt h=0$.
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