Hess流形上几何流的孤子
On solitons of a geometric flow on Hessian manifolds
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中文总结 AI 辅助
本文针对Hess流形上的几何流，引入Koszul孤子并研究其方程、性质与实例，通过关联仿射流形与复流形的方法拓展了几何问题的研究，该孤子在统计学与信息几何中具应用潜力。
中文摘要 AI 辅助
本研究引入Hesse-Koszul流的Koszul孤子，即Hess流形上某几何流的自相似解。我们得到了Koszul孤子的若干偏微分方程与基本性质，并给出了若干实例。核心思路是探究仿射流形与复流形的关系，该方法也可用于研究Hess流形上的其他几何问题。值得注意的是，Hess流形作为仿射流形的特例，在统计学与信息几何中具有广泛应用。
英文摘要
In this work, we introduce the Koszul solitons of the Hesse-Koszul flow, i.e., self-similar solutions for a geometric flow on Hessian manifolds. We obtain some partial differential equations and basic properties of Koszul solitons, and provide some examples. The key idea is to investigate the relationship between affine manifolds and complex manifolds, this method can also be used to study some other geometric problems on Hessian manifolds. It is worth noting that Hessian manifolds, as a special case of affine manifolds, have wide applications in statistics and information geometry.
