Extrinsic geometric properties of the Rozendorn surface, an isometric immersion of the Lobachevskiĭ plane in E5

© 2009 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation Yurii A Aminov 2009 Sb. Math. 200 1575 DOI 10.1070/SM2009v200n11ABEH004051

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

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1064-5616/200/11/1575

Abstract

The lengths of the normal curvature vectors on the Rozendorn surface  are shown to be uniformly bounded above on the whole of the surface. A regular three-dimensional submanifold , , is constructed in the form of a regular leaf whose sectional curvatures in the two-dimensional directions tangent to  are strictly negative and bounded away from zero.

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