Geodesic
Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface
Sbornik. Mathematics, Tome 26 (1975) no. 2, pp. 151-164

Voir la notice de l'article provenant de la source Math-Net.Ru

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. Bibliography: 20 titles. 
@article{SM_1975_26_2_a0,
     author = {L. L. Beskorovainaya},
     title = {Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface},
     journal = {Sbornik. Mathematics},
     pages = {151--164},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_26_2_a0/}
}
TY  - JOUR
AU  - L. L. Beskorovainaya
TI  - Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface
JO  - Sbornik. Mathematics
PY  - 1975
SP  - 151
EP  - 164
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1975_26_2_a0/
LA  - en
ID  - SM_1975_26_2_a0
ER  - 
%0 Journal Article
%A L. L. Beskorovainaya
%T Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface
%J Sbornik. Mathematics
%D 1975
%P 151-164
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1975_26_2_a0/
%G en
%F SM_1975_26_2_a0
L. L. Beskorovainaya. Canonical $A$-deformations preserving the lengths of lines of curvature on a~surface. Sbornik. Mathematics, Tome 26 (1975) no. 2, pp. 151-164. http://geodesic.mathdoc.fr/item/SM_1975_26_2_a0/