Canonical connections and their conformal invariants on Riemannian almost-product manifolds. (English) Zbl 0810.53026

Staikova, M. T.; Gribachev, K. I.

Serdica 18, No. 1-4, 150-161 (1992).

Summary: On a Riemannian \(P\)-manifold there is no complete analogy with the conformal geometry on a Riemannian manifold. In this paper, we consider a class of Riemannian almost-product manifolds (including Riemannian \(P\)- manifold). The general conformal group and its special subgroups are determined. It is shown that the Bochner curvature tensor of the manifold is a conformal invariant. It is proved that the zero Bochner curvature tensor is an integrability condition of a geometrical system of partial differential equations and a characterization condition of a conformally flat manifold, there is a complete analogy with the conformal geometry on a Riemannian manifold. Similar problems are considered in [G. Ganchev, K. Gribachev and V. Mihova, Publ. Inst. Math., Nouv. Ser. 42(56), 107-121 (1987; Zbl 0638.53021)] for a complex manifold with \(B\)-metric.

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C20	Global Riemannian geometry, including pinching

Keywords:

conformal geometry; Riemannian almost-product manifolds; Bochner curvature tensor; conformal invariant; conformally flat manifold

Citations:

Zbl 0638.53021