Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator

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dc.creatorFerapontov, E. V.
dc.date2001-07-17
dc.date.accessioned2026-07-07T04:42:38Z
dc.date.available2026-07-07T04:42:38Z
dc.descriptionThe class of surfaces in 3-space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We review some of the known examples and results, demonstrate the integrability of the corresponding Gauss-Codazzi equations and draw parallels between this geometrical problem and the theory of compatible Poisson brackets of hydrodynamic type. It turns out that coordinate hypersurfaces of the n-orthogonal systems arising in the theory of compatible Poisson brackets of hydrodynamic type must necessarily possess deformations preserving the shape operator.
dc.description17 pages, to appear in the Proccedings of the conference "Integrable Systems in Differential Geometry", Tokyo, July 2000
dc.identifierhttps://arxiv.org/abs/math/0107122
dc.identifierhttp://arxiv.org/abs/math/0107122
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61864
dc.subjectDifferential Geometry
dc.titleSurfaces in 3-space possessing nontrivial deformations which preserve the shape operator
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