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.
Citation: Jinhua Qian, Jie Liu, Xueshan Fu, Seoung Dal Jung. Geometric characterizations of canal surfaces with Frenet center curves[J]. AIMS Mathematics, 2021, 6(9): 9476-9490. doi: 10.3934/math.2021551
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.
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Jinhua Qian, Jie Liu, Xueshan Fu, Seoung Dal Jung. Geometric characterizations of canal surfaces with Frenet center curves[J]. AIMS Mathematics, 2021, 6(9): 9476-9490. doi: 10.3934/math.2021551
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