Weierstrass Representation of Lightlike Surfaces in Lorentz-Minkowski 4-Space

Authors : Davor DEVALD, Z MİLİN SİPUS

Pages : 232-243

Doi:10.36890/iejg.1272924

View : 62 | Download : 7

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :We present a Weierstrass-type representation formula which locally represents every regular two-dimensional lightlike surface in Lorentz-Minkowski 4-Space $\\mathbb{M}^4$ by three dual functions $insert ignore into journalissuearticles values(\\rho,f,g);$ and generalizes the representation for regular lightlike surfaces in $\\mathbb{M}^3$. We give necessary and sufficient conditions on the functions $\\rho$, $f$, $g$ for the surface to be minimal, ruled or $l$-minimal. For ruled lightlike surfaces, we give necessary and sufficient conditions for the representation itself to be ruled. Furthermore, we give a result on totally geodesic half-lightlike surfaces which holds only in $\\mathbb{M}^4$.
Keywords : Weierstrass representation, lightlike surface, minimal surface, conformal parametrization, ruled surface, Lorentz Minkowski 4 Space

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