We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the $\unicode[STIX]{x1D70C}$-connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold $P$ is endowed with a complex projective structure then $P$ can be locally identified, through quaternionic diffeomorphisms, with the quaternionic projective space.

中文翻译：

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投影结构和连接

我们将 TY Thomas 的方法扩展到复杂分析范畴上的射影结构，通过涉及$\unicode[STIX]{x1D70C}$-连接。这样，可以更好地控制投影平坦度，因此，我们有例如以下应用：如果四元数流形的扭量空间$P$被赋予复杂的射影结构，那么$P$可以通过四元数微分同胚与四元数射影空间局部识别。