Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 20-38
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A. A. Borisenko (jr.). On the structure of 3-dimensional minimal parabolic surfaces in Euclidean space. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 20-38. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a4/
@article{ZNSL_1996_234_a4,
author = {A. A. Borisenko (jr.)},
title = {On the structure of 3-dimensional minimal parabolic surfaces in {Euclidean} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {20--38},
year = {1996},
volume = {234},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a4/}
}
TY - JOUR
AU - A. A. Borisenko (jr.)
TI - On the structure of 3-dimensional minimal parabolic surfaces in Euclidean space
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1996
SP - 20
EP - 38
VL - 234
UR - http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a4/
LA - en
ID - ZNSL_1996_234_a4
ER -
%0 Journal Article
%A A. A. Borisenko (jr.)
%T On the structure of 3-dimensional minimal parabolic surfaces in Euclidean space
%J Zapiski Nauchnykh Seminarov POMI
%D 1996
%P 20-38
%V 234
%U http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a4/
%G en
%F ZNSL_1996_234_a4
It is shown that the structure of a three-dimensional minimal parabolic surface is determined by the pair $(V^2,\gamma)$, where $V^2$ is a minimal two-dimensional surface in $S^n$ and $\gamma$ satisfies $\Delta\gamma+2\gamma=0$ (here $\Delta$ is the Laplace operator in $R^n$). It is also shown that the singularities of the surface are determined by zeros of $\gamma$. Bibl. 9 titles.
