Generalized constant ratio hypersurfaces in Euclidean spaces

Nurettin Cenk Turgay

Generalized constant ratio hypersurfaces in Euclidean spaces

Differential Geometry 2015-04-30 v1

Authors: Nurettin Cenk Turgay

Abstract

In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in $\mathbb E^4$ . First, we deal with $\delta(2)$ -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, $\delta(r)$ -invariant hypersurfaces, constant mean curvature, Gauss-Kronecker curvature

Keywords

hypersurfaces surfaces with constant mean curvature differential geometry of surfaces and curves in euclidean space

Cite

@article{arxiv.1504.07757,
  title  = {Generalized constant ratio hypersurfaces in Euclidean spaces},
  author = {Nurettin Cenk Turgay},
  journal= {arXiv preprint arXiv:1504.07757},
  year   = {2015}
}

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