This article is cited in 2 scientific papers (total in 2 papers)
Canonical $A$-deformations preserving the lengths of lines of curvature on a surface
L. L. Beskorovainaya
In this paper, infinitesimal deformations which preserve the area element of a surface in $E_3$ ($A$-deformations) which also preserve the lengths of lines of curvature are studied. Here $A$-deformations are considered up to infinitesimal bendings (which constitute the trivial case for the problem posed). Such $A$-deformations are also called canonical.
For regular surfaces of nonzero total curvature (without umbilic points) the problem indicated reduces to a homogeneous second order partial differential equation of elliptic type. In this paper a series of results about the existence and arbitrariness of canonical $A$-deformations is obtained. The basic results are valid for surfaces in the large.
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Mathematics of the USSR-Sbornik, 1975, 26:2, 151–164
MSC: Primary 53A05; Secondary 35J25, 73L99
L. L. Beskorovainaya, “Canonical $A$-deformations preserving the lengths of lines of curvature on a surface”, Mat. Sb. (N.S.), 97(139):2(6) (1975), 163–176; Math. USSR-Sb., 26:2 (1975), 151–164
Citation in format AMSBIB
\paper Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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V. T. Fomenko, “A property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space”, Math. Notes, 59:2 (1996), 201–204
Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566
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