SURFACES IN E-3 WITH L-1-POINTWISE 1-TYPE GAUSS MAP

Kim Y. H. , Turgay N. C.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.50, no.3, pp.935-949, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.4134/bkms.2013.50.3.935
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.935-949

Abstract

In this paper, we study surfaces in E-3 whose Gauss map G satisfies the equation square G = f(G + C) for a smooth function f and a constant vector C, where square stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation square G = lambda(G + C) for a constant lambda and a constant vector C.