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Connections functorially attached to almost complex product structures

Fernando Etayo·Rafael Santamaría
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Abstract

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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Fernando Etayo, Rafael Santamaría. 2006-03-27. Connections functorially attached to almost complex product structures. https://arxiv.org/abs/math/0502319

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