Constant curvature factorable surfaces in 3-dimensional isotropic space
Muhittin Evren Aydin
TL;DR
This paper classifies factorable surfaces in 3D isotropic space with constant Gaussian and mean curvature, providing non-existence results for certain curvature ratios and illustrating examples.
Contribution
It offers a comprehensive classification of such surfaces and introduces new non-existence results for surfaces with specific curvature ratios.
Findings
Classification of factorable surfaces with constant K and H
Non-existence of surfaces with H/K=const.
Examples illustrating the classified surfaces.
Abstract
In this paper, we study factorable surfaces in a 3-dimensional isotropic space. We classify such surfaces with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result related with the surfaces satisfying H/K=const. Several examples are also illustrated.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Advanced Numerical Analysis Techniques