New criterion for the analyticity of a function: representation via the metric tensors of the surfaces $Z = u, Z = v$

• Date: 2019
• Main Authors: Bezkorovaina, L. L., Безкоровайная, Л. Л.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1460
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 514.75:517.53 We establish a new criterion for the analyticity of a function $w=u+iv$ or $\overline{w}=u-iv,$ $u(x, y),$ $v(x, y) \in C^1(G)$ in the domain $G.$ It is expressed via the metric tensors of the surfaces $Z=u$ and $Z=v\colon g_{11}-a_{22}=0,$ $g_{12}+a_{12} =0,$ $g_{22}-a_{11...