The Energy Functional of $$G_2$$ G 2 -Structures Compatible with a Background Metric
The Energy Functional of
$$G_2$$
G
2
-Structures Compatible with a Background Metric
复制标题
$$G_2$$ G 2 的能量泛函 - 与背景度量兼容的结构
DOI：
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发表时间：
2019
影响因子：
1.1
通讯作者：
Leonardo Bagaglini
中科院分区：
文献类型：
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作者：
Leonardo Bagaglini
$$G_2$$ G 2 结构的空间自然地由与固定黎曼度量兼容的那些结构分层。我们研究了对这些地层起作用的总扭转能量的限制。准确地说，我们展示了其负梯度流的短时存在性，我们用旋量场来表征其临界点的空间，最后，我们描述了均匀负梯度流的长期行为。
The space of $$G_2$$ G 2 -structures is naturally stratified by those structures compatible with a fixed Riemannian metric. We study the restriction of the total torsion energy functional to these strata. Precisely we show the short-time existence of its negative gradient flow, we characterise the space of its critical points in terms of spinor fields and, finally, we describe the long-time behaviour of the homogeneous negative gradient flow.