摘要翻译：
利用Cartan-Kahler理论和实代数结构的结果，我们证明了两个嵌入定理。首先，光滑紧致3-流形的内部可以等距嵌入到作为结合子流形的G2流形中。其次，光滑紧致4-流形K的内部可等距嵌入作为Cayley子流形的自旋（7）-流形。同时，我们还证明了关于光滑微分形式的实解析逼近的Bochner定理，可以用Akbulut和King发展的实代数工具得到。
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英文标题：
《Calibrated associative and Cayley embeddings》
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作者：
Colleen Robles and Sema Salur
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Differential Geometry        微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Using the Cartan-Kahler theory, and results on real algebraic structures, we prove two embedding theorems. First, the interior of a smooth, compact 3-manifold may be isometrically embedded into a G_2-manifold as an associative submanifold. Second, the interior of a smooth, compact 4-manifold K, whose double has a trivial bundle of self-dual 2-forms, may be isometrically embedded into a Spin(7)-manifold as a Cayley submanifold. Along the way, we also show that Bochner's Theorem on real analytic approximation of smooth differential forms, can be obtained using real algebraic tools developed by Akbulut and King.
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PDF链接：
https://arxiv.org/pdf/0708.1286