Geometric properties of some classes of Riemannian almost-product manifolds
In a recent paper, the reviewer has defined 36 different classes of Riemannian almost-product manifolds by the properties of the tensor field \(\nabla P\), \(P\) being the almost-product structure, \(\nabla\) the Levi-Civita connection [Rend. Mat. Appl., VII. Ser. 3, 577--592 (1983; Zbl 0538.53045) (see the second review below)]. In this paper the author defines four algebraic conditions for a distribution on a Riemannian manifold which are sufficient to describe the 36 classes, so simplifying the study of the geometric properties of the classes notably. In particular, the interpretation of many of the classes is given here by finding the geometric meaning of the four properties. The behaviour of the different classes under conformal transformations of the metric is studied by determining how the four conditions are transformed when the metric is conformally changed.
scientific article; zbMATH DE number 3855925
scientific article