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The Hypersurfaces with Parallel M(o)ebius Form in Sn+1
Author(s): ZHANG Tingzuo
Pages: 230-
238
Year: 2003
Issue:
2
Journal: ADVANCES IN MATHEMATICS
Keyword: Moebius形式; 平行; Blaschke张量; 迷向超曲面;
Abstract: 如果x:M→Sn+1是不合脐点的超曲面,且M的Moebius形式φ=0和Blaschke张量A=λg,就称M为Moebius迷向超曲面,如果x:M→Sn+1是不含脐点的超曲面,且M的Moebius形式φ平行( φ=0)和Blaschke张量A=λg,就称M为Moebius拟迷向超曲面,这里g是M上的Moebius度量,λ:M→R是M上的光滑函数,本文证明了如下结果:(1)设x:M→Sn+1(n≥3)是不合脐点的超曲面,则M是拟迷向超曲面当且仅当M是迷向超曲面,(2)设x:M→Sn+1(n≥3)是不含脐点的超曲面,且M的Moebius形式φ平行和Blaschke张量A也平行( A=0),则φ=0.
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