 Extrinsic curvature with a negative shift

For $d{s}^2=-N^{2}d{t}^2+h_{ij}(d{x}^i-N^{i}dt)(d{x}^j-N^{j}dt)$ and the future unit normal, the convention $K_{ij}=-n_{i;j}$ gives $K_{ij}=-({\dot{h}}_{ij}+D_i{N}_j+D_j{N}_i)/(2N)$. Lower the shift vector with $h$. The sign of the shift terms changes when the opposite threading convention is used.