Bj\"orling problem for timelike surfaces in the Lorentz-Minkowski space
Rosa M. B. Chaves, Martha P. Dussan, Martin Magid
TL;DR
This paper introduces a split-complex representation for timelike minimal surfaces in Lorentz-Minkowski space, solving the Bj"orling problem and characterizing special classes of these surfaces with new formulas and examples.
Contribution
It presents a novel split-complex approach to timelike minimal surfaces, solving the Bj"orling problem and characterizing specific surface types in Lorentz-Minkowski space.
Findings
Solved the Bj"orling problem for timelike surfaces
Derived new characterizations of minimal surfaces of revolution
Provided explicit examples of timelike minimal surfaces
Abstract
We introduce a new approach to the study of timelike minimal surfaces in the Lorentz-Minkowski space through a split-complex representation formula for this kind of surface. As applications, we solve the Bj\"orling problem for timelike surfaces and obtain interesting examples and related results. Using the Bj\"orling representation, we also obtain characterizations of minimal timelike surfaces of revolution as well as of minimal ruled timelike surfaces in the Lorentz-Minkowsi space.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Algebraic and Geometric Analysis · Advanced Differential Geometry Research