English

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

R2 v1 2026-06-22T12:28:30.431Z