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arXiv · 1908.02393

G1 structures on flag manifolds

Luciana A. Alves·Neiton Pereira da Silva
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Abstract

Let $U/K_\Theta$ be a generalized flag manifold, where $K_\Theta$ is the centralizer of a torus in $U$. We study $U$-invariant almost Hermitian structures on $U/K_\Theta$. The classification of these structures are naturally related with the system $R_t$ of t-roots associated to $U/K_\Theta$. We introduced the notion of connectedness by triples zero sum in a general set of linear functional and proved that t-roots are connected by triples zero sum. Using this property, the invariant G1 structures on $U/K_\Theta$ are completely classified. We also study the K\"ahler form and classified the invariant quasi K\"ahler structures on $U/K_\Theta$, in terms of t-roots.

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Luciana A. Alves, Neiton Pereira da Silva. 2019-08-06. G1 structures on flag manifolds. https://arxiv.org/abs/1908.02393

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