由不可积的特殊拉格朗日振动引起的g2度量

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-01-17 DOI:10.1515/coma-2019-0019

Ryohei Chihara

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引用次数: 3

摘要

摘要研究了SU(3)-流形的特殊拉格朗日振动，这些流形不一定是无扭的。在光纤为单模李群G的情况下，我们将这种SU(3)-结构分解为3流形上主G束上的焊接1-形式、连接1-形式和等变3 × 3正定对称矩阵值函数的三元组。作为应用，我们描述了在G = T3和SO(3)的情况下，约束动力系统在三元组空间上允许拉格朗日型三维群作用的g2流形的正则部分。

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G2-metrics arising from non-integrable special Lagrangian fibrations

Abstract We study special Lagrangian fibrations of SU(3)-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group G, we decompose such SU(3)-structures into triples of solder 1-forms, connection 1-forms and equivariant 3 × 3 positive-definite symmetric matrix-valued functions on principal G-bundles over 3-manifolds. As applications, we describe regular parts of G2-manifolds that admit Lagrangian-type 3-dimensional group actions by constrained dynamical systems on the spaces of the triples in the cases of G = T3 and SO(3).

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.