Buscher dual of a metric with vanishing two-form ($g_{ij}^{\prime }=g_{ij}-g_{yi}{g}_{yj}/g_{yy}$)

For a nondegenerate isometry direction $y$ and initially zero two-form, the local T-dual fields in alpha-prime-one units are $g_{yy}^{\prime }=1/g_{yy}$, $g_{yi}^{\prime }=0$, $g_{ij}^{\prime }=g_{ij}-g_{yi}{g}_{yj}/g_{yy}$, $B_{yi}^{\prime }=g_{yi}/g_{yy}$ and $B_{ij}^{\prime }=0$. Gauging the isometry and eliminating its auxiliary connection derives these rules. The spectator metric is a Schur complement. The sign of the mixed two-form follows the multiplier and dual-coordinate orientation convention.