An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into $E^6$ with a section as the Veronese surface

Yu. A. Aminov^a, O. A. Goncharova<sup>b

a</sup> Technical University in Bialystok, Wiejska 45, Bialystok, Poland; On leave from Inst. for Low Temperature of NAN of the Ukraine, Lenin Ave. 47, 310164, Kharkov, Ukraine
^b Kharkov State University, 4 Svobody Sq., 310077, Kharkov, Ukraine

Abstract: 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.

Received: 03.03.1998

Language: English

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