This article is cited in 5 papers

On Isometric Immersions with Flat Normal Connection of the Hyperbolic Space $L^n$ Into Euclidean Space $E^{n+m}$

D. V. Bolotov

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

Abstract: We prove that the hyperbolic space $L^n$ cannot be immersed in an Euclidean space $E^{n+m}$ with a flat normal connection provided the module of the mean curvature vector is bounded.

Keywords: immersion, mean curvature, principal directions, flat normal connection, hyperbolic space, Grassmanian image, quasiisometric space.

UDC: 514.132

Received: 10.03.2006
Revised: 05.12.2006

DOI: 10.4213/mzm3748

 English version: Mathematical Notes, 2007, 82:1, 10–12

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