Bezkorovaina L. L.
Surfaces generated by the real and imaginary parts of analytic functions: $A$-deformations occurring independently or simultaneously
Ukr. Mat. Zh. - 2018. - 70, № 4. - pp. 447-463
It is proved that the surfaces generated by the real and imaginary parts of analytic functions allow nontrivial infinitesimal areal deformations of certain three types. The fields of displacements are explicitly expressed in all three cases. Given surfaces are rigid with respect to infinitesimal bendings of each type.
Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 878–884
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.