Differential Geometry and its Applications ( IF 0.5 ) Pub Date : 2020-06-04 , DOI: 10.1016/j.difgeo.2020.101647 N. Ando
Space-like surfaces and time-like surfaces with zero mean curvature vector in oriented neutral 4-manifolds are isotropic and compatible with the orientations of the spaces if and only if their lifts to the space-like and the time-like twistor spaces respectively are horizontal. In neutral Kähler surfaces and paraKähler surfaces, complex curves and paracomplex curves respectively are such surfaces and characterized by one additional condition. In neutral 4-dimensional space forms, the holomorphic quartic differentials defined on such surfaces vanish. There exist time-like surfaces with zero mean curvature vector and zero holomorphic quartic differential which are not compatible with the orientations of the spaces and the conformal Gauss maps of time-like surfaces of Willmore type and their analogues give such surfaces.
中文翻译:
中性流形为零且曲率向量为零的曲面
定向中性4流形中具有零平均曲率向量的类空表面和时类表面是各向同性的,并且当且仅当它们分别向类空间和类时间扭曲空间提升时才与该类空间兼容。水平。在中性Kähler曲面和paraKähler曲面中,复曲线和超复曲线分别是这样的曲面,并且具有一个附加条件。在中性4维空间形式中,在此类曲面上定义的全纯四次微分消失。存在具有零平均曲率向量和零全同性四次微分的时态表面,它们与空间的方向不兼容,Willmore类型时态表面及其类似物的共形高斯图给出了这样的表面。