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We consider a covariant symmetric tensor $T_f$ $=$ ${\\displaystyle f^*h - \\frac{1}{m} |df|^2 g}$, where $f^*h$ denotes the pull-back metric of $h$ by $f$. The tensor $T_f$ vanishes if and only if the map $f$ is weakly conformal. The norm $|T_f|$ is a quantity which is a measure of conformality of $f$ at each point. We are concerned with maps which are critical points of the functional $\\Phi (f)$ $=$ ${\\displaystyle \\int_M |T_f|^2dv_g}$. 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