具有传递约化自同构群的闭$\ mathm {G}_2$-结构

IF 0.5 4区数学 Q3 MATHEMATICS

Asian Journal of Mathematics Pub Date : 2019-11-29 DOI:10.4310/AJM.2021.v25.n6.a6

F. Podestà, Alberto Raffero

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引用次数: 0

摘要

.我们给出了具有闭的非平行G2-结构并允许自同构的传递还原群G的七维流形的完全分类。特别地，我们证明了G的中心是一维的，并且流形是一个因子和一个非紧齐次六维流形的黎曼乘积，该流形被赋予SU（3）-结构的不变的严格辛半流形。

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Closed $\mathrm{G}_2$-structures with a transitive reductive group of automorphisms

. We provide the complete classiﬁcation of seven-dimensional manifolds endowed with a closed non-parallel G 2 -structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a ﬂat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-ﬂat SU(3)-structure.

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