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

  • L. L. Bezkorovaina
  • T. Yu. Vashpanova

Abstract

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 $A$-deformations with stationary lengths of LGT-lines.
Published
25.07.2010
How to Cite
Bezkorovaina, L. L., and T. Y. Vashpanova. “$A$-Deformations of a Surface With Stationary Lengths of $LGT$-Lines”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 7, July 2010, pp. 878–884, https://umj.imath.kiev.ua/index.php/umj/article/view/2921.
Section
Research articles