Compact closed hyper-surfaces in the positive curvature space form are studied.By using a known integral formula,the totally umbilical property of compact closed hyper-surfaces with constant mean curvature is proved.The result gives an uniqueness conclusion for hyper-surfaces of this type.%设 Mn 是单位球面 S n+1(1)中的紧致闭超曲面，且 Mn 及其 Gauss 映照像均落在 Sn+1(1)的一个开半球面内。利用一个已知的积分公式，证明了：如果 Mn 的平均曲率 H 1是常数，则 Mn 是全脐的。
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