Weierstrass representation for lightlike surfaces in Lorentz-Minkowski 3-space

Devald, Davor; Šipuš, Željka Milin

doi:10.1016/j.geomphys.2021.104252

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…For regular light-like surfaces, they are locally parameterized with a pair of holomorphic and meromorphic dual functions. Moreover, the definition of minimal light-like surfaces in Lorentz-Minkowski three-dimensional space is also discussed on this basis, and it is related to the class of surfaces characterized by the Weierstrass representation formula [4]. In addition to this, in another paper by Davor, he extended the formula for the Weierstrass representation of the minimal class of time-like surfaces in Minkowski threedimensional space found by S. Lee to the same surfaces in Minkowski four-dimensional space [5].…”

Section: Introductionmentioning

confidence: 99%

Weierstrass Representation of Minimal Surfaces and Related Basic Quantities

Zhang

2024

HSET

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Minimal surface, as an important surface in differential geometry, has long been one of the research topics of many scholars. It provides far-reaching research materials for geometric analysis and nonlinear partial differential equations, and plays an important role in mathematical general relativity. The minimal surface mentioned in this paper refers to the surface with the smallest area when the boundary conditions remain unchanged, i.e., the Plateau problem. The physical counterpart is the soap film experiment. It is different from a surface of constant mean curvature in another sense. Weierstrass discovered that the general solution of minimal surface equations can be given by complex analysis, that is, Weierstrass representation of minimal surface, thus revealing the essential relationship between minimal surface and holomorphic function and meromorphic function. In this paper, the Weierstrass representation of minimal surface is organized, and the first and second basic forms of minimal surface are derived by using its complex vector form. The study of minimal curved surface has played an important role in many fields such as construction engineering, material science and so on.

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Section: Introductionmentioning

confidence: 99%

Weierstrass Representation of Minimal Surfaces and Related Basic Quantities

Zhang

2024

HSET

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

DEVALD¹,

Šipuš

2023

International Electronic Journal of Geometry

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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 $(\rho,f,g)$ 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 $\mathbb{M}^4$.

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Weierstrass representation for lightlike surfaces in Lorentz-Minkowski 3-space

Cited by 2 publications

References 7 publications

Weierstrass Representation of Minimal Surfaces and Related Basic Quantities

Weierstrass Representation of Minimal Surfaces and Related Basic Quantities

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

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