常曲率空间S^(n+p)(C)中的紧致极小子流形

A compact mininal submanifold of constant curvature space S^(n+p)(C)

设Mn是常曲率空间Sn+p(C)的紧致极小子流形,Q是Mn上每点各方向Ricci曲率的下确界,σ为Mn的第二基本形式长度的平方。利用Mn的内在量Q和σ给出了常曲率空间Sn+p(C)中紧致极小子流形是全测地子流形的几个充分条件。

Let Mn be an ndimensional compact minimal submanifold in Sn+p(C) with constant curvature C.Let Q be the infimum of the Ricci curvature of Mn and σ be the square of the length of the second fundamental form of Mn.Several sufficient conditions of Mn be the totally geodesic submanifold are obtained.