@article{Sato_2021, title={$d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$}, volume={52}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3045}, DOI={10.5556/j.tkjm.52.2021.3045}, abstractNote={<span>In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{</span><span id="MathJax-Element-3-Frame" class="MathJax"><span id="MathJax-Span-17" class="math"><span><span><span id="MathJax-Span-18" class="mrow"><span id="MathJax-Span-19" class="msubsup"><span><span><span id="MathJax-Span-20" class="texatom"><span id="MathJax-Span-21" class="mrow"><span id="MathJax-Span-22" class="mi">R}^{</span></span></span></span><span><span id="MathJax-Span-23" class="texatom"><span id="MathJax-Span-24" class="mrow"><span id="MathJax-Span-25" class="mn">0</span><span id="MathJax-Span-26" class="mo">,</span><span id="MathJax-Span-27" class="mn">2</span><span id="MathJax-Span-28" class="mo">,</span><span id="MathJax-Span-29" class="mn">1}$</span></span></span></span></span></span></span></span></span></span></span><span> endowed with a degenerate metric. We define $</span><span id="MathJax-Element-4-Frame" class="MathJax"><span id="MathJax-Span-30" class="math"><span><span><span id="MathJax-Span-31" class="mrow"><span id="MathJax-Span-32" class="mi">d$</span></span></span></span></span></span><span>-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $</span><span id="MathJax-Element-5-Frame" class="MathJax"><span id="MathJax-Span-33" class="math"><span><span><span id="MathJax-Span-34" class="mrow"><span id="MathJax-Span-35" class="mi">d$</span></span></span></span></span></span><span>-minimal surfaces in $\mathbb{<span id="MathJax-Element-3-Frame" class="MathJax"><span id="MathJax-Span-17" class="math"><span id="MathJax-Span-18" class="mrow"><span id="MathJax-Span-19" class="msubsup"><span id="MathJax-Span-20" class="texatom"><span id="MathJax-Span-21" class="mrow"><span id="MathJax-Span-22" class="mi">R}^{</span></span></span><span id="MathJax-Span-23" class="texatom"><span id="MathJax-Span-24" class="mrow"><span id="MathJax-Span-25" class="mn">0</span><span id="MathJax-Span-26" class="mo">,</span><span id="MathJax-Span-27" class="mn">2</span><span id="MathJax-Span-28" class="mo">,</span><span id="MathJax-Span-29" class="mn">1}$</span></span></span></span></span></span></span></span><span> and spacelike flat zero mean curvature (ZMC) surfaces in four-dimensional Minkowski space $\mathbb{<span id="MathJax-Element-3-Frame" class="MathJax"><span id="MathJax-Span-17" class="math"><span id="MathJax-Span-18" class="mrow"><span id="MathJax-Span-19" class="msubsup"><span id="MathJax-Span-20" class="texatom"><span id="MathJax-Span-21" class="mrow"><span id="MathJax-Span-22" class="mi">R}^{4</span></span></span><span id="MathJax-Span-23" class="texatom"><span id="MathJax-Span-24" class="mrow"><span id="MathJax-Span-29" class="mn">}_{1}$</span></span></span></span></span></span></span></span><span> are in one-to-one correspondence.</span>}, number={1}, journal={Tamkang Journal of Mathematics}, author={Sato, Yuichiro}, year={2021}, month={Jan.}, pages={37–67} }