Flat Surfaces in the Euclidean Space E-3 with Pointwise 1-Type Gauss Map

Dursun U.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.33, no.3, pp.469-478, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 3
  • Publication Date: 2010
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.469-478
  • Istanbul Technical University Affiliated: No

Abstract

In this article we prove that a fiat nonplanar surface in the Euclidean space E-3 with pointwise 1-type Gauss map of the second kind is either a right circular cone or a cylinder such that the curvature of the base curve satisfies a specific differential equation. We conclude that there is no tangent developable surface in E-3 with pointwise 1-type Gauss map of the second kind.