This article is cited in 4 papers

Geometry of the Grassmann image of a local isometric immersion of Lobachevskii $n$-dimensional isometric immersion of Lobachevskii $n$-dimensional

Yu. A. Aminov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Abstract: In this paper we obtain an expression for the curvature tenser of the metric of the Grassmann image of an isometric immersion of Lobachevskii $n$-dimensional space in $(2n-1)$-dimensional Euclidean space. The main result is the following theorem: there is no $C^3$ local isometric immersion of 3-dimensional Lobachevski space in 5-dimensional Euclidean space with constant curvature of the metric of the Grassmann image.

UDC: 514

MSC: Primary 53C42; Secondary 53A35, 53C20

Received: 06.06.1995

DOI: 10.4213/sm184

 English version: Sbornik: Mathematics, 1997, 188:1, 1–27

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