A Kind Of Minimal Surface Under Pseudo-orthogonal Frames

Compared with Euclidean space,Minkowski space is a fire-new field.Because of the difference of its metric from Euclidean space’s,many essential concepts in Minkowski space change a lot。This makes the conclusions of some problems in Minkowski space much different.It also provides the direction for our research.This article will mainly focus on discussing rotating surfaces in Minkowski space.The rotation surfaces discussed in this article are generalizations of Minimal Surfaces,in the case of which a lot of remarkable conclusions have been found.At the same time,it is a plane curve around the fixed axis of rotation,along with the corresponding another light curve to do the parallel transport.In this article,we mainly discuss the generation of curved surface when a plane curve is rotated around the optical axis and parallels to any type of the light curve.Mainly discussed whether it can make a minimal surface and compared with helicoidal surface of the same or different,for the convenience of calculation we used pseudo-orthogonal frame.By the calculations we discovered that there are only a few types of surfaces with mean curvature of zero.There are two types of helical surfaces,which have been studied.So our work is to select a plane curve,while it rotated along the fixed optical axis,moving along a special curve in parallel.