Fedchenko J. Infinitesimal geodesic deformations of surfaces

The thesis is devoted to investigation of infinitesimal geodesic deformations of surfaces. For such type of deformations the new forms of the basic equations on components of a vector of displacement and their tensors are found. Special infinitesimal geodesic deformations of surfaces are studied. Necessary and sufficient conditions for existence of such type deformations are found. Deformations of revolution surfaces as well as deformations of minimal surfaces and surfaces of constant Gauss curvature are described. A formal integrability condition for the system of basic equations of infinitesimal geodesic deformations of metrics is given and estimates for dimensions of solution spaces are found.