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arXiv · 1705.10397

On Weyl-reducible conformal manifolds and lcK structures

Farid Madani·Andrei Moroianu·Mihaela Pilca
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Abstract

A recent result of M. Kourganoff states that if $D$ is a closed, reducible, non-flat, Weyl connection on a compact conformal manifold $M$, then the universal covering of $M$, endowed with the metric whose Levi-Civita covariant derivative is the pull-back of $D$, is isometric to $\mathbb{R}^q\times N$ for some irreducible, incomplete Riemannian manifold $N$. Moreover, he characterized the case where the dimension of $N$ is $2$ by showing that $M$ is then a mapping torus of some Anosov diffeomorphism of $T^{q+1}$. We show that in this case one necessarily has $q=1$ or $q=2$.

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Farid Madani, Andrei Moroianu, Mihaela Pilca. 2017-05-29. On Weyl-reducible conformal manifolds and lcK structures. https://arxiv.org/abs/1705.10397

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