Modified Laplacian coflow of G₂-structures on manifolds with symmetry

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• 作者：Sergey Grigorian ^{sergey.grigorian@utrgv.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C25 ; 53C29 ; 53C44
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：46
• 期：Complete
• 页码：39-78
• 全文大小：646 K

文摘

We consider G₂$G_2$-structures on 7-manifolds that are warped products of an interval and a six-manifold, which is either a Calabi–Yau manifold, or a nearly Kähler manifold. We show that in these cases the G₂$G_2$-structures are determined by their torsion components. We then study the modified Laplacian coflow c357958c4917a6e8ef19cf12">$\frac{d\psi }{dt}={\mathrm{\Delta }}_{\psi }\psi +2d\left((C-\mathrm{Tr}T)\phi \right)$ of these G₂$G_2$-structures, where φ and ψ   are the fundamental 3-form and 4-form which define the G₂$G_2$-structure and Δ_ψ${\mathrm{\Delta }}_{\psi }$ is the Hodge Laplacian associated with the G₂$G_2$-structure. This flow is known to have short-time existence and uniqueness. We analyze the soliton equations for this flow and obtain new compact soliton solutions.