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arXiv · 1611.05608

Affine translation hypersurfaces in Euclidean and isotropic spaces

Muhittin Evren Aydin
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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.

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Muhittin Evren Aydin. 2016-11-17. Affine translation hypersurfaces in Euclidean and isotropic spaces. https://arxiv.org/abs/1611.05608

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