Geodesic
MG-deformations of a surface of positive Gaussian curvature under assignment of variation of any tensor along an edge
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 16-23

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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 this boundary-value problems is reduced to the investigation of a solvability of Riemann–Gilbert boundary-value problem and to calculation of its index. As a result we get theorems of existence and uniqness for the infinitesimal MG-deformation.
Keywords: infinitesimal MG-deformations, simply-connected surface, Riemann–Gilbert boundary-value problem, index. 
@article{IVM_2017_12_a1,
     author = {D. A. Zhukov},
     title = {MG-deformations of a surface of positive {Gaussian} curvature under assignment of variation of any tensor along an edge},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--23},
     publisher = {mathdoc},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_12_a1/}
}
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D. A. Zhukov. MG-deformations of a surface of positive Gaussian curvature under assignment of variation of any tensor along an edge. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 16-23. http://geodesic.mathdoc.fr/item/IVM_2017_12_a1/