2013/01/01 by A. Rod Gover, Paweł Nurowski
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.1215/ijm/1408453588
crossref issued 2013/01/01 · crossref published 2013/01/01 · crossref published-print 2013/01/01 · openalex publication_date 2013/01/01 · crossref created 2019/03/01 · crossref deposited 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · crossref indexed 2026/07/29
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.