$A$-deformations of a surface with stationary lengths of $LGT$-lines

• Date: 2010
• Main Authors: Bezkorovaina, L. L., Vashpanova, T. Yu., Безкоровайна, Л. Л., Вашпанова, Т. Ю.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2921
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate infinitesimal areal deformations ($A$-deformations) of the first order under which the lengths of $LGT$-lines of a surface are preserved in the $E_3$ -space. We prove that any regular surface of the class $C^4$ of nonzero Gaussian curvature without umbilical points admits nontrivial $...