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arXiv · 1706.06401

Special homogeneous almost complex structures on symplectic manifolds

Alberto Della Vedova
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Abstract

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be covered by co-adjoint orbits. Conversely, compact isotropy co-adjoint orbits of semi-simple Lie groups are shown to admit special compatible almost complex structures whenever they satisfy a necessary topological condition. Some classes of examples including twistor spaces of hyperbolic manifolds and discrete quotients of Griffiths period domains of weight two are discussed.

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Alberto Della Vedova. 2017-06-20. Special homogeneous almost complex structures on symplectic manifolds. https://doi.org/10.4310/jsg.2019.v17.n5.a1

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