CHARACTERIZATION OF THE HELICOID AS RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

  • Choi, Mie-Kyung (DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCE, KYUNGPOOK NATIONAL UNIVERSITY) ;
  • Kim, Young-Ho (DEPARTMENT OF MATHEMATICS, TEACHERS COLLEGE, KYUNGPOOK NATIONAL UNIVERSITY)
  • Published : 2001.01.01

Abstract

We introduce the notion of Gauss map of pointwise 1-type on ruled surfaces in the Euclidean 3-space for which vector valued functions is neither trivial nor it extends or coincides with the usual notion of 1-type, in general. We characterize the minimal helicoid in terms of it and give a complete classification of the ruled surfaces with pointwise 1-type Gauss map.

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