Spacelike surfaces in \(\mathbb{L}^4\) with null mean curvature vector and the nonlinear Riccati partial differential equation

DOI10.1016/j.na.2021.112271zbMath1464.53082OpenAlexW3126680732WikidataQ114146031 ScholiaQ114146031MaRDI QIDQ2019305

Yanyan Li

Publication date: 20 April 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2021.112271

zbMATH Keywords

Weierstrass representationspace-like surfaceLorentz-Minkowski spacelight conenonlinear Riccati partial differential equation

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Quasi-analytic and other classes of functions of one complex variable (30D60)

Related Items (2)

Explicit solving of the system of natural PDEs of minimal Lorentz surfaces in \(\mathbb{R}_2^4\) ⋮ Spacelike minimal surfaces which are graphs in \(\mathbb{R}_1^4\)

Cites Work

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• The Gauss map of surfaces in \(\mathbb R^ n\)
• Surfaces in the lightlike cone
• Hypersurfaces in lightlike cone
• Newton’s laws of motion in the form of a Riccati equation
• The geometry of the generalized Gauss map
• Curvature properties of zero mean curvature surfaces in four-dimensional Lorentzian space forms
• Minimal surfaces in euclidean 3-space and their mean curvature 1 cousins in hyperbolic 3-space
• Björling problem for maximal surfaces in Lorentz–Minkowski space

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