I always wonder how the definitions of curvatures of curves and surfaces be unified by the Riemann Tensor symbols.(adsbygoogle = window.adsbygoogle || []).push({});

For surfaces, I know R_{1,2,1,2} corresponds to the Gaussian curvature of a surface. How come R_{1,1,1,1}=0 and not corresponds to the curvature of a curve in \RE^2 or in \Re^3 ?

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# About curvature

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