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PROJECTIVE STRUCTURES AND $\unicode[STIX]{x1D70C}$-CONNECTIONS

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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,… Click to show full abstract

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.

Keywords: x1d70c connections; projective structures; structures unicode; stix x1d70c; unicode stix

Journal Title: Journal of the Institute of Mathematics of Jussieu
Year Published: 2018

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