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Bi-Lagrangian structures on nilmanifolds. (arXiv:1810.06518v1 [math.SG])
来源于:arXiv
We study bi-Lagrangian structures (a symplectic form with a pair of
complementary Lagrangian foliations, also known as para-K\"ahler or K\"unneth
structures) on nilmanifolds of dimension less than or equal to 6. In
particular, building on previous work of several authors, we determine which
6-dimensional nilpotent Lie algebras admit a bi-Lagrangian structure. In
dimension 6, there are (up to isomorphism) 26 nilpotent Lie algebras which
admit a symplectic form, 16 of which admit a bi-Lagrangian structure and 10 of
which do not. We also calculate the curvature of the canonical connection of
these bi-Lagrangian structures. 查看全文>>