Connections functorially attached to almost complex product structures

Details Connections functorially attached to almost complex product structures Connections functorially attached to almost complex product structures

2005-02-15

arxiv.org/abs/math/0502319v2

Houston J. Math. 35, No. 2, 411-434 (2009)

Mathematics

Differential Geometry

sections 3 and 4 rewritten and simplified, added subsection 4.1 and updated references

Scientific paper

Manifolds endowed with three foliations pairwise transversal are known as 3-webs. Equivalently, they can be algebraically defined as biparacomplex or complex product manifolds, i.e., manifolds endowed with three tensor fields of type $(1,1)$, $F$, $P$ and $J=F \circ P$, where the two first are product and the third one is complex, and they mutually anti-commute. In this case, it is well known that there exists a unique torsion-free connection parallelizing the structure. In the present paper, we study connections attached to non-integrable almost biparacomplex manifolds.

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