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

Part of: Local differential geometry Classical differential geometry Global differential geometry

Published online by Cambridge University Press:  22 March 2018

Radu Pantilie
Radu Pantilie*
Affiliation:
Institutul de Matematică “Simion Stoilow” al Academiei Române, C.P. 1-764, 014700, Bucureşti, România (radu.pantilie@imar.ro)
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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

complex projective structures𝜌-connections

MSC classification

Primary: 53A20: Projective differential geometry 53B10: Projective connections 53C56: Other complex differential geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 2 , March 2020 , pp. 571 - 579
Copyright
© Cambridge University Press 2018

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Footnotes

The author acknowledges partial financial support from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project no. PN-III-P4-ID-PCE-2016-0019.

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