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


Kim Y. H. , Turgay N. C.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.50, no.4, pp.1345-1356, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.4134/bkms.2013.50.4.1345
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1345-1356

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(1)G = f (G + C) for some constant vector C is an element of E-3 and smooth function f, where L-1 denotes the Cheng-Yau operator.