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arXiv · 2404.13253

Reduction of coK\"{a}hler and 3-cosymplectic manifolds

Shuhei Yonehara
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Abstract

The notions of coK\"{a}hler manifolds and 3-cosymplectic manifolds are odd-dimensional analogues of the ones of K\"{a}hler manifolds and hyperK\"{a}hler manifolds, respectively. In this paper, we obtain reduction theorems of coK\"{a}hler manifolds and 3-cosymplectic manifolds. We show that K\"{a}hler and coK\"{a}hler (hyperK\"{a}hler and 3-cosymplectic) reductions admit a natural compatibility with respect to ``cylinder constructions". We further prove the compatibility of K\"{a}hler and coK\"{a}hler reductions with respect to the "mapping torus construction".

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Shuhei Yonehara. 2024-04-20. Reduction of coK\"{a}hler and 3-cosymplectic manifolds. https://doi.org/10.7546/jgsp-68-2024-59-80

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