On the Ruled Surfaces with L1-Pointwise 1-Type Gauss Map

<p>Young Ho Kim<br />Nurettìn Cenk Turgay</p>

doi:10.5666/KMJ.2017.57.1.133

Article

Kyungpook Mathematical Journal 2017; 57(1): 133-144

Published online March 23, 2017

On the Ruled Surfaces with L₁-Pointwise 1-Type Gauss Map

Young Ho Kim¹
Nurettìn Cenk Turgay²

Department of Mathematics, Kyungpook National University, Daegu 41566, Korea¹
Department of Mathematics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey²

Received: June 18, 2014; Accepted: October 17, 2014

Abstract

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Abstract

In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying □G = f(G+C) for a constant vector C ∈ and a smooth function f, where □ denotes the Cheng-Yau operator.

Keywords: Cheng-Yau operator, Gauss map, null scroll, pointwise 1-type, ruled surface