If we have that for geodesic they satisfy...(adsbygoogle = window.adsbygoogle || []).push({});

[tex] S=\int_{a}^{b}ds\sum_{a,b}(\dot{x_{a}\dot{x^{b}) [/tex]

then minimizing the functional we get the geodesic equation..my question is if for the Area of a Surface is:

[tex] A=\iint_{S}dA\sum_{a,b}(f_{a})(f_{b}) [/tex]

wherewehave defined [tex] f_{a}=df/dx_{a} [/tex]

then my questions are..

-you can see that thes definitions can be generalized to the case we have a non-euclidean metric g_ab, What would be the equation that gets the minimum of the surface?...

-What is the "Geodesic surface" (MInimal surface) equation depending on the connections and the metric?..does is satisfy that [tex] \nabla{f} [/tex] where f is the surface and "nabla" is the COvariant derivative.

-What is the equivalent of the [tex] R_{ab} [/tex] tensor for our minimal surface?..thanks...note the minimizes J or J^{1/2} you get almost the same results in the practise.

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# MInimal surfaces

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