Almost Kaehler geometry of adjoint orbits of semisimple Lie groups

Alberto Della Vedova; Alice Gatti

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arXiv · 1811.06958

Almost Kaehler geometry of adjoint orbits of semisimple Lie groups

Alberto Della Vedova·Alice Gatti

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Abstract

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the Chern-Ricci form, the Hermitian scalar curvature and the Nijenhuis tensor in terms of root data. We also discuss when the Chern-Ricci form is a multiple of the symplectic form, and when compact quotients of these orbits are of Kaehler type.

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Alberto Della Vedova, Alice Gatti. 2018-11-26. Almost Kaehler geometry of adjoint orbits of semisimple Lie groups. https://arxiv.org/abs/1811.06958

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