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CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP

  • Received : 2012.10.12
  • Published : 2013.07.31

Abstract

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

Keywords

Gauss map;$L_1$-pointwise 1-type;Cheng-Yau operator;rotational surface;helicoidal surface;Lie point symmetry

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Cited by

  1. RULED SURFACES AND GAUSS MAP vol.52, pp.5, 2015, https://doi.org/10.4134/BKMS.2015.52.5.1661
  2. Invariant surfaces with pointwise 1-type Gauss map in Sol3 vol.106, pp.3, 2015, https://doi.org/10.1007/s00022-015-0261-7
  3. Classifications of Canal Surfaces with L1-Pointwise 1-Type Gauss Map vol.83, pp.1, 2015, https://doi.org/10.1007/s00032-015-0233-2
  4. Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map vol.36, pp.3, 2018, https://doi.org/10.5269/bspm.v36i3.31263

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)