In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of th...In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of the two smallest eigenvalues of curvature operator are bounded below by δ.scal 〉 O. If we relax the restriction of positivity of complex sectional curvature to non- negativity, we can also show that the manifold is compact under the additional condition of positive asymptotic volume ratio.展开更多
文摘In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of the two smallest eigenvalues of curvature operator are bounded below by δ.scal 〉 O. If we relax the restriction of positivity of complex sectional curvature to non- negativity, we can also show that the manifold is compact under the additional condition of positive asymptotic volume ratio.
