An example of isometric immersion of a domain of 3-dimensional Lobachevsky space into E6 with a section as the Veronese surface

Анотація

Some example of isometric immersion of a domain of the Lobachevsky space L³ into E⁶ is constructed in such a way that every intersection of the obtained submanifold with coordinate hyperplane x⁶=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 L³ into E^k, k > 5, in the form of special submanifolds.