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arXiv · 1802.06315

Center of mass and Kähler structures

Scott O. Wilson·Mahmoud Zeinalian
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Abstract

There is a sequence of positive numbers $δ_{2n}$, such that for any connected $2n$-dimensional Riemannian manifold $M$, there are two mutually exclusive possibilities: $1)$ There is a complex structure on $M$ making it into a Kähler manifold, or $2)$ For any almost complex structure $J$ compatible with the metric, at every point $p\in M$, there is a smooth loop $γ$ at $p$ such that $dist(J_p, hol_γ^{-1}J_phol_γ)> δ_{2n}$.

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Scott O. Wilson, Mahmoud Zeinalian. 2018-02-18. Center of mass and Kähler structures. https://arxiv.org/abs/1802.06315

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