论文标题
tachibana型定理完全歧管
Tachibana-type theorems on complete manifolds
论文作者
论文摘要
我们证明，与谐波曲率和$ \ lfloor \ frac {m-1} {2} {2} \ rfloor $ - 阳性曲率操作员具有恒定的截面曲率，具有恒定的截面曲率，具有良好的Tachibana theorem for Spartold corporolds for Sportold operator的正面曲率。 $ \ lfloor \ frac {m-1} {2} \ rfloor $ - postitivity的状况源自彼得森和温克的最新作品，他们证明了类似的tachibana-type定理，在更强的条件下，歧义是爱因斯坦。我们表明，假设抛物线，在Weyl张量上的积分键或更强的点上下限，则具有相同的刚度属性。对于3个体而言，我们表明曲率操作员的阳性可以放松至RICCI张量的阳性。
We prove that a compact Riemannian manifold of dimension $m \geq 3$ with harmonic curvature and $\lfloor\frac{m-1}{2}\rfloor$-positive curvature operator has constant sectional curvature, extending the classical Tachibana theorem for manifolds with positive curvature operator. The condition of $\lfloor\frac{m-1}{2}\rfloor$-positivity originates from recent work of Petersen and Wink, who proved a similar Tachibana-type theorem under the stronger condition that the manifold be Einstein. We show that the same rigidity property holds for complete manifolds assuming either parabolicity, an integral bound on the Weyl tensor or a stronger pointwise positive lower bound on the average of the first $\lfloor\frac{m-1}{2}\rfloor$ eigenvalues of the curvature operator. For 3-manifolds, we show that positivity of the curvature operator can be relaxed to positivity of the Ricci tensor.
