允许反对称Ricci张量的射影曲面的局部障碍
Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor
摘要：
决定一个射影结构是否在其给定的具有斜对称Ricci张量的射影类中允许一个联络的方程是一个超定的半线性偏微分方程系统，我们称之为射影Einstein-Weyl（pEW）方程。在2维空间中，我们给出了射影曲面在其射影类中接纳这种连接的局部障碍。障碍物是多项式方程的结果，这些多项式方程必须被满足以允许任何pEW解。
英文摘要：
The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions for projective surfaces to admit such a connection in its projective class. The obstructions are the resultants of polynomial equations that have to be satisfied for there to admit any pEW solution.
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