Deformations in G2 manifolds
Deformations in G2 manifolds
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G2 流形中的变形
DOI：
10.1016/j.aim.2007.09.009
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发表时间：
2008
影响因子：
1.7
通讯作者：
S. Salur
中科院分区：
文献类型：
--
作者：
S. Akbulut;S. Salur
本文研究了具有标定3-形式φ的G2流形M7中结合子流形的变形。选择M上的2-平面场Λ（它总是存在），将M的切丛分裂为一个3维缔合丛和一个复4-平面丛TM=E V的直和，这有助于我们将形变与Seiberg-Witten型方程联系起来。本文仅用叉积运算（等价于φ）证明了关于G2流形的已有结果和新结果.我们认为，混合各种不同的局部标识丰富的G2几何（例如，交叉产品，表示理论和代数的八元数）使研究G2流形看起来更难，然后它是（例如，证明姆克林的定理[R.C.姆克林，校准子流形的变形，Comm. Anal。6（1998）705-747]）。我们相信这里的方法使事情变得更容易，并保持演示的基本性。
Here we study the deformations of associative submanifolds inside a G2manifold M7with a calibration 3-form φ. A choice of 2-plane field Λ on M (which always exists) splits the tangent bundle of M as a direct sum of a 3-dimensional associate bundle and a complex 4-plane bundle TM=E⊕V, and this helps us to relate the deformations to Seiberg–Witten type equations. Here all the surveyed results as well as the new ones about G2manifolds are proved by using only the cross product operation (equivalently φ). We feel that mixing various different local identifications of the rich G2geometry (e.g. cross product, representation theory and the algebra of octonions) makes the study of G2manifolds look harder then it is (e.g. the proof of McLean's theorem [R.C. McLean, Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998) 705–747]). We believe the approach here makes things easier and keeps the presentation elementary.