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

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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.

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Author information

Correspondence to L. L. Bezkorovaina.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 878–884, July, 2010.

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Bezkorovaina, L.L., Vashpanova, T.Y. A-deformations of a surface with stationary lengths of LGT-lines. Ukr Math J 62, 1018–1027 (2010). https://doi.org/10.1007/s11253-010-0410-y

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Keywords

  • Minimal Surface
  • Principal Direction
  • Deformation Tensor
  • Regular Surface
  • Umbilical Point