Geodesic
A~property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 284-290.

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

It is proved that conformal infinitesimal deformations of a surface $F^k$ in Riemannian space, and they only, are areally recurrent infinitesimal deformations. All areally recurrent deformations of the hypersphere $S^{n-1}$ in $E^n$ are described. 
@article{MZM_1996_59_2_a13,
     author = {V. T. Fomenko},
     title = {A~property of conformal infinitesimal deformations of multidimensional surfaces in {Riemannian} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {284--290},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a13/}
}
TY  - JOUR
AU  - V. T. Fomenko
TI  - A~property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space
JO  - Matematičeskie zametki
PY  - 1996
SP  - 284
EP  - 290
VL  - 59
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a13/
LA  - ru
ID  - MZM_1996_59_2_a13
ER  - 
%0 Journal Article
%A V. T. Fomenko
%T A~property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space
%J Matematičeskie zametki
%D 1996
%P 284-290
%V 59
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a13/
%G ru
%F MZM_1996_59_2_a13
V. T. Fomenko. A~property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 284-290. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a13/

[1] Rashevskii P. K., Rimanova geometriya, Nauka, M., 1964

[2] Beskorovainaya L. L., “Kanonicheskie $A$-deformatsii, sokhranyayuschie dliny linii krivizny poverkhnosti”, Matem. sb., 93:2 (1975), 163–176

[3] Fomenko L. P., “$A^2$-deformatsii poverkhnostei $F^k$ v $E^n$”, Sib. matem. zh., 32:5 (1991), 204; Деп. ВИНИТИ, No 5543–В90 | Zbl

[4] Chen B. Y., Yano K., “On the theory of normal variations”, J. Diff. Geom., 13 (1978), 1–10 | MR | Zbl