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Center of mass and Kähler structures

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Zeinalian,  Mahmoud
Max Planck Institute for Mathematics, Max Planck Society;

Fulltext (public)

arXiv:1802.06315.pdf
(Preprint), 98KB

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Citation

Wilson, S. O., & Zeinalian, M. (2019). Center of mass and Kähler structures. Journal of Geometry, 110(2): 33.

Cite as: http://hdl.handle.net/21.11116/0000-0007-8D46-C
Abstract
There is a sequence of positive numbers $\delta_{2n}$, 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 K\"ahler manifold, or $2)$ For any almost complex structure $J$ compatible with the metric, at every point $p\in M$, there is a smooth loop $\gamma$ at $p$ such that $dist(J_p, hol_\gamma^{-1}J_phol_\gamma)> \delta_{2n}$.