Illinois Journal of Mathematics

Calculus and invariants on almost complex manifolds, including projective and conformal geometry

A. Rod Gover and Paweł Nurowski

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We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In particular, we are able to construct an invariant and efficient calculus for conformal almost Hermitian geometries, and also for almost complex structures that are equipped with a projective structure. In the latter case, we find a projectively invariant tensor the vanishing of which is necessary and sufficient for the existence of an almost complex connection compatible with the path structure. In both the conformal and projective setting, we give torsion characterisations of the canonical connections and introduce certain interesting higher order invariants.

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Illinois J. Math., Volume 57, Number 2 (2013), 383-427.

First available in Project Euclid: 19 August 2014

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Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C05: Connections, general theory 53A20: Projective differential geometry 53A30: Conformal differential geometry 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)


Gover, A. Rod; Nurowski, Paweł. Calculus and invariants on almost complex manifolds, including projective and conformal geometry. Illinois J. Math. 57 (2013), no. 2, 383--427. doi:10.1215/ijm/1408453588.

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