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Static almost-Kähler structures on Lie groups

Camilla Molina

Universidad Nacional de Córdoba, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak51fc72eee6d97501ebcf818c7ca3d073').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy51fc72eee6d97501ebcf818c7ca3d073 = 'm&#111;l&#105;n&#97;c&#97;m&#105;ll&#97;' + '&#64;'; addy51fc72eee6d97501ebcf818c7ca3d073 = addy51fc72eee6d97501ebcf818c7ca3d073 + 'h&#111;tm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text51fc72eee6d97501ebcf818c7ca3d073 = 'm&#111;l&#105;n&#97;c&#97;m&#105;ll&#97;' + '&#64;' + 'h&#111;tm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak51fc72eee6d97501ebcf818c7ca3d073').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy51fc72eee6d97501ebcf818c7ca3d073 + '\'>'+addy_text51fc72eee6d97501ebcf818c7ca3d073+'<\/a>';

The symplectic curvature flow is a specially sophisticated equation that evolves almost-Kähler manifolds. The fixed points of this flow, which are analogous to the Einstein metrics for the Ricci flow, are called static structures. Streets and Tian, who first introduced the flow, proved that in dimension $4$ every compact smooth manifold with a static structure is Kähler-Einstein. We show that this rigidity condition is no longer valid in dimension $6$ and above.