$A$-deformations of a surface with stationary lengths of $LGT$-lines
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.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1018-1027.
Citation Example: Bezkorovaina L. L., Vashpanova T. Yu. $A$-deformations of a surface with stationary lengths of $LGT$-lines // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 878–884.