Also known as the first fundamental form, d s^2 = g_(a b) d x^a d x^b. In the principal axis frame for three dimensions, d s^2 = g_11 (d x^1)^2 + g_22 (d x^2)^2 + g_33 (d x^3)^2. At ordinary points on a surface, the line element is positive definite.
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