论文标题
$ \ MATHBB {S}^6 $（或任何$ \ Mathbb {s}^2 \ times \ Mathbb {s}^4 $，$ \ Mathbb {s}^2 \ times \ times \ Mathbb {s}^6 $}对复杂的歧管的差异
$\mathbb{S}^6$ (or any of $\mathbb{S}^2 \times \mathbb{S}^4$, $\mathbb{S}^2\times\mathbb{S}^6$, or $\mathbb{S}^6\times \mathbb{S}^6$, respectively) is not diffeomorphic to a complex manifold
论文作者
论文摘要
我们在封闭的$ n $ manifold上识别所有指标，并将其NASH等距嵌入到一个大的但固定的尺寸的标准球体中，并使用palais的同位素扩展理论来识别其嵌入的同位素变形的变形，其嵌入的同位素变形，在其构造中识别出与相应的Isotopics conformit cenformations conformations neforpifications sejections sejectif seformal issotic seplotic seploctip。如果$ n \ geq 3 $，我们将以恒定标态曲率的指标来表征其相关嵌入的外在量的属性，并证明在恒定正与标曲率曲率的歧管上的任何度量都可以将其最小化到该背景领域中，这是其配置类别的Yamabe Metric。然后，我们使用Simons的间隙定理来研究Yamabe指标的几乎复杂的遗传变形的外在数量，标准的最小值几乎复杂的等距嵌入$ \ mb {s}^6 $，$ \ mb {s}^6 $，$ \ mb {s}} $ \ mb {s}^2 \ times \ mb {s}^6 $和$ \ mb {s}^6 \ times \ mb {s}^6 $，并证明这些歧视都不携带可携带的集成几乎复杂的几乎复杂的结构。 ：
We identify all metrics on a closed $n$-manifold with their Nash isometric embeddings into a standard sphere of large, but fixed dimension, and use the Palais' isotopic extension theorem to identify their deformations with the isotopic deformations of their embeddings, the deformations of metrics in a conformal class identified with their corresponding isotopic conformal deformations. If $n\geq 3$, we characterize metrics of constant scalar curvature in terms of properties of extrinsic quantities of their associated embeddings, and prove that any metric on the manifold of constant positive scalar curvature, which can be minimally embedded into this background sphere, is a Yamabe metric in its conformal class. We then use Simons' gap theorem to study the extrinsic quantities of almost complex Hermitian deformations, by Yamabe metrics, of the standard minimal almost complex isometric embeddings of $\mb{S}^6$, $\mb{S}^2 \times \mb{S}^4$, $\mb{S}^2\times\mb{S}^6$, and $\mb{S}^6\times \mb{S}^6$, respectively, and prove that none of these manifolds carry integrable almost complex structures. :
