MG-deformations of a surface of positive Gaussian curvature under assignment of variation of any tensor along an edge |
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Authors: | D. A. Zhukov |
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Affiliation: | 1.Southern Federal University,Rostov-on-Don,Russia |
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Abstract: | We investigate the infinitesimal MG-deformations of a simply connected surface with positive Gaussian curvature. We choose any symmetric tensor on the surface, variation of the first and the second invariant of this tensor equals given function along a boundary. The study of these boundary-value problems is reduced to the investigation of a solvability of Riemann–Hilbert boundary-value problem and to calculation of its index. As a result we get theorems of existence and uniqueness for the infinitesimal MG-deformation. |
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