Classification results on surfaces in the isotropic 3-space
Differential Geometry
2017-06-05 v1
Abstract
The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in I^3 with the constant relative curvature (analogue of the Gaussian curvature) and the constant isotropic mean curvature. In particular, we classify the helicoidal surfaces in I^3 with constant curvature and analyze some special curves on these.
Keywords
Cite
@article{arxiv.1601.03190,
title = {Classification results on surfaces in the isotropic 3-space},
author = {Muhittin Evren Aydin},
journal= {arXiv preprint arXiv:1601.03190},
year = {2017}
}
Comments
12 pages, 2 figures