# Vekua method

*in the theory of infinitesimal deformations*

A method which can be applied to the case when certain quantities which characterize the deformation of surfaces with positive Gaussian curvature $ K $ are, in a conjugate-isothermal parametrization, generalized analytic functions (cf. Generalized analytic function). This makes it possible to reduce the study of the deformation of surfaces with variable $ K > 0 $ to a definite problem concerning surfaces with $ K = \textrm{ const } > 0 $, whose infinitesimal deformations (cf. Infinitesimal deformation) are described by ordinary analytic functions, thus establishing a far-reaching analogy between the properties of deformations of surfaces with variable and constant positive Gaussian curvature.

#### References

[1] | I.N. Vekua, "Generalized analytic functions" , Pergamon (1962) (Translated from Russian) |

**How to Cite This Entry:**

Vekua method.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Vekua_method&oldid=49143