USING OF CARTAN'S MOVING FRAME METHOD IN DIFFERENTIAL GEOMETRY OF SURFACES

Milos Kanka

Abstract


The aim of this paper is to give basic geometrical characteristics of sphere and torus, parameterization of which is , but our interest is concentrated mainly to Cobb-Douglas surfaces used in economics. We are going to study these functions as regular surfaces in R3. Applying the method of Cartan moving frame we obtain geometrical description of Cobb-Douglas function  used in economy, parameterization of which has the form

,   where ,  u > 0  , v > 0  and .


Keywords


Orthonormal frame, tangent space, differential forms, Gaussian curvature, Maurer-Cartan equations, Cartan’s lemma.

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References


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