Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 3-9
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Yu. A. Aminov; O. A. Goncharova. An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into $E^6$ with a section as the Veronese surface. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a0/
@article{JMAG_1999_6_1_a0,
author = {Yu. A. Aminov and O. A. Goncharova},
title = {An example of isometric immersion of a domain of 3-dimensional {Lobachevsky} space into $E^6$ with a section as the {Veronese} surface},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {3--9},
year = {1999},
volume = {6},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a0/}
}
TY - JOUR
AU - Yu. A. Aminov
AU - O. A. Goncharova
TI - An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into $E^6$ with a section as the Veronese surface
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 1999
SP - 3
EP - 9
VL - 6
IS - 1
UR - http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a0/
LA - en
ID - JMAG_1999_6_1_a0
ER -
%0 Journal Article
%A Yu. A. Aminov
%A O. A. Goncharova
%T An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into $E^6$ with a section as the Veronese surface
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 1999
%P 3-9
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a0/
%G en
%F JMAG_1999_6_1_a0
Some example of isometric immersion of a domain of the Lobachevsky space $L^3$ into $E^6$ is constructed in such a way that every intersection of the obtained submanifold with coordinate hyperplane $x^6=const$ be the Veronese surface. The submanifold is not orientable and admits a $2$-parametric family of motions along itself. It is also proved general statements on existence of immersions of some domain of $L^3$ into $E^k$, $k>5$, in the form of special submanifolds.
