Difference between revisions of "Vekua method"
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''in the theory of infinitesimal deformations'' | ''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 | + | 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|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|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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.N. Vekua, "Generalized analytic functions" , Pergamon (1962) (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.N. Vekua, "Generalized analytic functions" , Pergamon (1962) (Translated from Russian)</TD></TR></table> | ||
Latest revision as of 08:28, 6 June 2020
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
Vekua method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Vekua_method&oldid=49143
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article