Geometric characterizations of canal surfaces with Frenet center curves

Abstract

In this work, we study the canal surfaces foliated by pseudo hyperbolic spheres $ \mathbb{H}_{0}^{2} $ along a Frenet curve in terms of their Gauss maps in Minkowski 3-space. Such kind of surfaces with pointwise 1-type Gauss maps are classified completely. For example, an oriented canal surface that has proper pointwise 1-type Gauss map of the first kind satisfies $ \Delta \mathbb{G} = -2K\mathbb{G}, $ where $ K $ and $ \mathbb{G} $ is the Gaussian curvature and the Gauss map of the canal surface, respectively.

Keywords

• canal surface
• gauss map
• laplace operator
• pseudo hyperbolic sphere
• minkowski 3-space