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complex projective structures

Journal of the Institute of Mathematics of Jussieu (1)

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PROJECTIVE STRUCTURES AND $\unicode[STIX]{x1D70C}$-CONNECTIONS
Part of
Radu Pantilie
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 2 / March 2020

Published online by Cambridge University Press:

22 March 2018, pp. 571-579

Print publication:

March 2020
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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, 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.