Canonical connection and the canonical conformal group on a Riemannian almost-product manifold. (English) Zbl 0709.53024

Let \(M_{2n}\) be a manifold with an almost-product structure (P,g) and let \(\tilde g\) be the associated metric. The author defines an action of the fundamental group of the structure (P,g) on the bundle \({\mathcal T}\) of tensors of type (0,3) which are skew-symmetric in the first two arguments and determines a decomposition of the bundle \({\mathcal T}\) in the direct sum of four invariant and orthogonal subbundles. Then he shows that there exists a unique linear connection \(\nabla\) compatible with the structure (P,g) whose torsion tensor field T belongs to \({\mathcal T}_ 1\oplus {\mathcal T}_ 3\). Finally the author proves that the group of the general conformal transformations of the metric g generates a group of conformal transformations of the canonical connection \(\nabla\).
Reviewer: V.Cruceanu


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C10 \(G\)-structures