تقرير
Convergence of the hypersymplectic flow on $T^4$ with $T^3$-symmetry
| العنوان: | Convergence of the hypersymplectic flow on $T^4$ with $T^3$-symmetry |
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| المؤلفون: | Fine, Joel, He, Weiyong, Yao, Chengjian |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Symplectic Geometry, 58J35, 53C26, 53D05 |
| الوصف: | A hypersymplectic structure on a 4-manifold is a triple $\omega_1, \omega_2, \omega_3$ of 2-forms for which every non-trivial linear combination $a^1\omega_1 + a^2 \omega_2 + a^3 \omega_3$ is a symplectic form. Donaldson has conjectured that when the underlying manifold is compact, any such structure is isotopic in its cohomolgy class to a hyperk\"ahler triple. We prove this conjecture for a hypersymplectic structure on $T^4$ which is invariant under the standard $T^3$ action. The proof uses the hypersymplectic flow, a geometric flow which attempts to deform a given hypersymplectic structure to a hyperk\"ahler triple. We prove that on $T^4$, when starting from a $T^3$-invariant hypersymplectic structure, the flow exists for all time and converges modulo diffeomorphisms to the unique cohomologous hyperk\"ahler structure. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.15016 |
| رقم الأكسشن: | edsarx.2404.15016 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |