The recurrent areal spaces of the submetric class (Q1118169)

The author defines the recurrent areal spaces of the submetric class and discusses their properties. He proves that if an \(R^ p\)-recurrent \(A_ n^{(m)}\) areal space of the submetric class is decomposable, that is, it can be expressed as a product \(A_ 1^{(m)}\times A^{(m)}_{n-1}\) where the first factor is an \(R^ p\)-recurrent \(A_ 1^{(m)}\)-space and the other is an \(A^{(m)}_{n-1}\)-space with vanishing \(R^ p\)- curvature tensor. Also, he defines an \(R^ p\) (or \(k^ p\)-)symmetric areal space of the submetric class and studies its properties. At the end, he proves that in an \(R^ p\)-recurrent areal space of the submetric class admitting an areal motion, the recurrence vector field \(A_ 1\) behaves like a Lie invariant.