Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 309-333
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Vasil Gorkaviy. Theorem of reduction in the problem of reconstruction of submanifolds in Euclidean space by a given Grassmann image. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 309-333. http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a3/
@article{JMAG_1997_4_3_a3,
author = {Vasil Gorkaviy},
title = {Theorem of reduction in the problem of reconstruction of submanifolds in {Euclidean} space by a given {Grassmann} image},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {309--333},
year = {1997},
volume = {4},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a3/}
}
TY - JOUR
AU - Vasil Gorkaviy
TI - Theorem of reduction in the problem of reconstruction of submanifolds in Euclidean space by a given Grassmann image
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 1997
SP - 309
EP - 333
VL - 4
IS - 3
UR - http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a3/
LA - ru
ID - JMAG_1997_4_3_a3
ER -
%0 Journal Article
%A Vasil Gorkaviy
%T Theorem of reduction in the problem of reconstruction of submanifolds in Euclidean space by a given Grassmann image
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 1997
%P 309-333
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a3/
%G ru
%F JMAG_1997_4_3_a3
A necessary condition for the Grassmann image of submanifolds in the Euclidean space is proved. It is shown that the reconstruction of a submanifold $F^n\subset E^{n+m}$ with the constant dimension $l$ of the first normal space by a given $k$-dimensional Grassmann image $\Gamma$ is equivalent to the reconstruction of some submanifold $\tilde F^k\subset E^{k+l}$ with the constant dimension I of the first normal space by a given fe-dimensional Grassmann image $\tilde\Gamma$, where $\tilde\Gamma$ is connected with $\Gamma$ in a special way.
