极流形与环面流形
Polar and torus manifolds
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中文总结 AI 辅助
本文研究环面流形的极作用问题，证明拟toric流形可配备使环面作用为极的不变度量，且环面无穷小极作用满足商的实轨形欧拉类消失时可构造此类度量。
中文摘要 AI 辅助
我们证明了拟toric（拟环面）流形可配备一种不变度量，使得其上的环面作用是极的。更一般地，我们证明环面的无穷小极作用允许不变黎曼度量使其成为极作用，当且仅当其商的实orbifold（轨形）欧拉类消失。由于拟toric流形的轨道空间是可缩的简单多面体，该上同调障碍平凡消失。
英文摘要
We show that quasitoric manifolds can be equipped with an invariant metric for which the torus action is polar. More generally, we show that an infinitesimally polar action of a torus admits an invariant Riemannian metric making it polar if and only if the real orbifold Euler class of its quotient vanishes. Because the orbit spaces of quasitoric manifolds are contractible simple polytopes, this cohomological obstruction trivially vanishes.
