Generalized constant ratio hypersurfaces in Euclidean spaces

2015/04/29 by Nurettin Cenk Turgay, Turgay, Nurettin Cenk
Mathematics · #53B25 (Secondary) #53C42 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B25 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1504.07757

arxiv created 2015/04/29 · arxiv updated 2015/04/30

Abstract

In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in \mathbb E⁴. First, we deal with δ(2)-ideal GCR hypersurfaces. Then, we study on hypersurfaces with constant (first) mean curvature. Finally, we obtain the complete classification of GCR hypersurfaces with vanishing Gauss-Kronecker curvature. We also give some explicit examples. Keywords: Generalized constant ratio submanifolds, δ(r)-invariant hypersurfaces, constant mean curvature, Gauss-Kronecker curvature

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