Geometry of spacelike generalized constant ratio surfaces in Minkowski 3-space

Abstract

Generalized constant ratio surfaces are defined by the property that the tangential component of the position vector is a principal direction on the surfaces. In this work, we study these class of surfaces in the 3-dimensional Minkowski space {\mathbb{L}}^{\mathrm{3}}. We achieve a complete classification of spacelike generalized constant ratio surfaces in {\mathbb{L}}^{\mathrm{3}}.

Key words： Generalized constant ratio (GCR) surface; constant slope surface; constant ratio surface

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