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

  • Milos Kanka College of Polytechnics Jihlava
Keywords: Orthonormal frame, tangent space, differential forms, Gaussian curvature, Maurer-Cartan equations, Cartan’s lemma.

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 .

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Published
2012-12-01
Section
Articles