局部对称空间中的紧致极小子流形的Ricci曲率

Ricci Curvature of Compact Minimal Submanifolds in Locally Symmetric Space

设Nn+p是截面曲率KN满足1/2<δ≤K_N≥1的n+p维局部对称空间完备的δ-Pinching黎曼流形,Mn是Nn+p中的紧致极小子流形。讨论了这类子流形关于Ricci曲率的pinching问题。

Let N^n＋p be a n ＋ p-dimensional locally symmetric complete Riemannian manifold with 1 sectional curvature KN satisfies 1/2〈δ≤KN≤1 and M^n be an n-dimensional compact minimal submanifolds in N^n＋p. In this paper, the authors discuss the pinching theorem about this manifold with Ricci curvature.