Two interesting examples

Perdomo Oscar; Wei Guoxin

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Two interesting examples

Perdomo Oscar 1, Wei Guoxin 2 *

1. Department of Mathematics, Central Connecticut State University, New Britain 06050

2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631

*Correspondence author

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Funding: NSFC （No.Grant No. 11001087）, SRFDP （No.Grant No. 20104407120002）

Opened online:18 February 2014

Accepted by: none

Citation: Perdomo Oscar, Wei Guoxin.Two interesting examples[OL]. [18 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4585082

Firstly, we will show with an example that the completeness condition is needed in our result. Secondly, we will give an example of a complete hypersurface in $S^5$ with constant Gauss-Kronecker curvature that satisfies the condition $l_v=lambda f_v$ for some non zero $v$, which is neither a totally umbilical hypersurface nor a cartesian product of Euclidean spheres.

Keywords:Pure mathematics; manifold; curvature

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