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arXiv · 1601.03190

Classification results on surfaces in the isotropic 3-space

Muhittin Evren Aydin
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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.

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Muhittin Evren Aydin. 2016-01-13. Classification results on surfaces in the isotropic 3-space. https://doi.org/10.5578/fmbd.27735

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