具有三个不同主曲率的完备Dupin超曲面

DUPIN HYPERSURFACES WITH THREE DISTINCT PRINCIPAL CURVATURES

研究了Ｍ（ｃ）ｎ＋１（Ｃ≥０）中具常中曲率和三个不同主曲率的完备Ｄｕｐｉｎ超曲面等参的条件，得到：１）若Ｍ的数量曲率为常数，或２）λ１λ２λ３＝非零常数时，Ｍ等参。并较容易的获得了文［２］的一个结论。

Let M be a Dupin hypersurfaces of M(c)n+1 with constant mean curvature and with three distinct principal curvatures, We have the following theorems:Theorem I If the scalar curvature R=constant. then M be a isoparametric hypersurface of M(c)n+1. Theorem Ⅱ If λ1λ2λ3=constant≠0 then, M be a isoparametire hypersurface of M(c)n+1.