R_(1)^(4)中具有正则平坦嵌入端的零亏格的完备类空H=0曲面

On Spacelike Complete Stationary Genus 0 Surfaces with Regular Flat Embedded Ends in R_(1)^(4)

本文讨论R_(1)^(4)中具有正则平坦嵌入端的零亏格的类空H=0曲面.设k为正则平坦嵌入端的个数,我们证明,当k=l时,曲面为平面;当k=2,3时,不存在具有k个正则平坦嵌入端的类空H=0曲面.当k≠1,2,3,5,7时,我们给出两参数族的R_(1)^(4)中具有k个正则平坦嵌入端的例子.

This paper considers spacelike complete stationary genus 0 surfaces with regular flat embedded ends in R_(1)^(4).Let k be the number of regular flat embedded ends.We prove that when k=1,the surface is the plane;we also show that there exist no spacelike stationary genus 0 surfaces with k regular flat embedded ends when k=2,3.We give 2-family of examples of spacelike complete stationary genus 0 surfaces with k regular flat embedded ends in R_(1)^(4),when k≠1,2,3,5,7.