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 (SCI-Expanded) identifier identifier

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.