Geometry Of Functions In Economics (Application Of Cartan's Moving Frame Method)

  • Milos Kanka College of Polytechnics, Jihlava
  • Eva Kankova University of Ecomomics in Prague
Keywords: Orthonormal Moving Frame, Maurer-Cartan Structural Equations, Weingarten Map, Gaussian Curvature, Parametrized Utility Surface, Exterior Product, Exterior Differentiation

Abstract

Our principal object of study is the geometry of special sub-
manifolds of R
3
. The method we are going to use was in-
vented by Darboux and brought to perfection by Cartan. On
a Riemannian manifold (M; h; i) we define an orthonormal
moving frame (X
1
; : : : ; X
n
) such that (X
1
(p); : : : ; X
(p)
is an orthonormal frame for tangent space M
. The aim of
this article is to give geometrical analysis of a special type
of Cobb-Douglas surface, especially the formula of Gauss
curvature
(x; y) = (x; y; Ax
);
where

y

p
A = 1; x > 0; y > 0; = 1 or = 2 and = 1:
For this purpose we use the Cartan’s moving frame method.
n

References

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Published
2011-12-23
Section
Articles