Estimates and monotonicity for a heat flow of isometric $$G_{2}$$ G 2 -structures
Estimates and monotonicity for a heat flow of isometric $$G_{2}$$ G 2 -structures
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等轴 $$G_{2}$$ G 2 结构热流的估计和单调性
DOI：
10.1007/s00526-019-1630-0
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发表时间：
2019
影响因子：
2.1
通讯作者：
Grigorian, Sergey
中科院分区：
文献类型：
--
作者：
Grigorian, Sergey
给出一个7维紧致黎曼流形，它允许-结构，所有与该度量相容的-结构都被M上八元数丛的单位截面化。我们在单位八元数截面上定义了一个自然能量泛函，并考虑了与之相关的热流。这种泛函和流的临界点精确地对应于具有无散度扭转的结构。在这篇文章中，我们首先得到V(T)沿流的导数的估计，并证明只要挠率保持有界，流就存在。我们还证明了该流的一个单调性公式和一个正则性结果。最后，我们证明了在包含无挠结构的度量结构类中，在一定条件下，流将收敛到无挠结构。
Given a 7-dimensional compact Riemannian manifoldthat admits-structure, all the-structures that are compatible with the metricgare parametrized by unit sections of an octonion bundle overM. We define a natural energy functional on unit octonion sections and consider its associated heat flow. The critical points of this functional and flow precisely correspond to-structures with divergence-free torsion. In this paper, we first derive estimates for derivatives ofV(t) along the flow and prove that the flow exists as long as the torsion remains bounded. We also prove a monotonicity formula and an-regularity result for this flow. Finally, we show that within a metric class of-structures that contains a torsion-free-structure, under certain conditions, the flow will converge to a torsion-free-structure.