Affine translation hypersurfaces in Euclidean and isotropic spaces
Differential Geometry
2017-09-01 v3
Abstract
In this paper, we extend the notion of affine translation surfaces introduced by Liu and Yu (Proc. Japan Acad. Ser. A Math. Sci. 89, 111--113, 2013) in a Euclidean space R^{3} to higher dimensional ambient spaces. We provide that an affine translation hypersurface of constant Gauss-Kronocker curvature K_{0} in R^{n+1} is a cylinder, i.e. K_{0}=0. As further applications we describe such hypersurfaces in the isotropic spaces satisfying certain conditions on the isotropic curvatures and the Laplacian.
Keywords
Cite
@article{arxiv.1611.05608,
title = {Affine translation hypersurfaces in Euclidean and isotropic spaces},
author = {Muhittin Evren Aydin},
journal= {arXiv preprint arXiv:1611.05608},
year = {2017}
}
Comments
11 pages, no figure. Commets are all welcome