论文标题
带有$ 4 \ frac {1} {2} $的歧管 - 第二类的正曲率操作员
Manifolds with $4\frac{1}{2}$-positive curvature operator of the second kind
论文作者
论文摘要
我们表明，$ 4 \ frac {1} {2} $的封闭的四个manifold - 第二种的正弯曲操作员对球形空间形式是差异的。曲率假设非常清晰，因为$ \ mathbb {cp}^2 $和$ \ mathbb {s}^3 \ times \ times \ mathbb {s}^1 $具有$ 4 \ frac {1} {1} {2} $ - 第二种的非负曲率操作员。在较高的尺寸$ n \ geq 5 $中，我们表明，$ 4 \ frac {1} {2} $ 4的封闭riemannian歧管 - 第二种的正弯曲操作员是球形空间形式的同构。通过证明$ 4 \ frac {1} {2} $ - 第二类的正弯曲操作员意味着阳性的各向同性曲率和阳性RICCI曲率，证明了这些结果。还获得了第二种的非负曲率操作员的$ 4 \ frac {1} {1} {2} $。
We show that a closed four-manifold with $4\frac{1}{2}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. The curvature assumption is sharp as both $\mathbb{CP}^2$ and $\mathbb{S}^3 \times \mathbb{S}^1$ have $4\frac{1}{2}$-nonnegative curvature operator of the second kind. In higher dimensions $n\geq 5$, we show that closed Riemannian manifolds with $4\frac{1}{2}$-positive curvature operator of the second kind are homeomorphic to spherical space forms. These results are proved by showing that $4\frac{1}{2}$-positive curvature operator of the second kind implies both positive isotropic curvature and positive Ricci curvature. Rigidity results for $4\frac{1}{2}$-nonnegative curvature operator of the second kind are also obtained.
