R^4中具有常数量曲率的完备超曲面

Complete Hypersurfaces in R 4 with Constant Scalar Curvature and Mean Curvature

Ｒ４中具有常数量曲率Ｒ＝０及常中曲率Ｈ≠０的完备连通超曲面是否只有Ｓ１（１｜Ｈ｜）×Ｒ２？这一问题虽然已有讨论但事实上并没有得到彻底解决．本文证明了一个定理。

Is S 1(1|H|)×R 2 the only hypersurfaces in R 4 with scalar curvature R=0 and constant mean curvature H≠0? This question has been discussed but not solved completely.In the present paper,we prove a theorem which answers affirmatively the above question.