Abstract:
In this paper the following problem is solved: if in the Grassmann manifold G2,4 a regular submanifold Γ2 of dimension 2 is given, does there exist in Euclidean space E4 a regular surface F2 for which Γ2 is the Grassmann image? Sufficient conditions are found for this problem to have a solution and for it to be unique.
Bibliography: 9 titles.
\Bibitem{Ami82}
\by Yu.~A.~Aminov
\paper Defining a surface in 4-dimensional Euclidean space by means of its Grassmann image
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 2
\pages 155--168
\mathnet{http://mi.mathnet.ru/eng/sm2196}
\crossref{https://doi.org/10.1070/SM1983v045n02ABEH002592}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=644766}
\zmath{https://zbmath.org/?q=an:0509.53005|0487.53005}
Linking options:
https://www.mathnet.ru/eng/sm2196
https://doi.org/10.1070/SM1983v045n02ABEH002592
https://www.mathnet.ru/eng/sm/v159/i2/p147
This publication is cited in the following 3 articles:
V. A. Gorkavyy, “Reconstruction of a submanifold of Euclidean space from its Grassmannian image that degenerates into a line”, Math. Notes, 59:5 (1996), 490–497
A. A. Borisenko, Yu. A. Nikolaevskii, “Grassmann manifolds and the Grassmann image of submanifolds”, Russian Math. Surveys, 46:2 (1991), 45–94
Joel L. Weiner, “The Gauss map for surfaces in 4-space”, Math. Ann., 269:4 (1984), 541
Citation in format AMSBIB
Contact us: