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令Mn为n维子流形,其乘积的平均曲率H为Mm(c)×R,其中,Mm(c)具是截面曲率c为常数的空间型.通过利用Simons不等式,得到了一系列结果.“,”Let Mn be an n-dimensional submanifold with parallel mean curvature H of product space form Mm(c)×R,where Mm(c)is a space form with constant sectional curvature c.By using the method of Simons inequality,a series of results are obtained.