Spinor Representation in Isotropic 3-Space via Laguerre Geometry
Joseph Cho,
Dami Lee,
Wonjoo Lee
et al.
Abstract:We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface theory in isotropic space, we define spin transformations, directly leading to the spinor representation of conformal surfaces in isotropic space. As an application, we obtain the Weierstrass-type representation for zero mean curvature surfaces, and the Kenmotsu-type representation for constant mean curvature surfaces, allowing us to co… Show more
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