The paracomplex projective spaces as symmetric and natural spaces (Q1194643)

The authors continue to study the properties of the paracomplex projective spaces \(P_ r(B)\) [the authors, Pac. J. Math. 136, No. 1, 85- 101 (1989; Zbl 0706.53024); Rend. Semin. Fac. Sci. Univ. Cagliari 59, 131-145 (1989)]. They study \(P_ r(B)\) and the reduced paracomplex projective space as symmetric spaces. These spaces can also be considered as natural pseudo-Riemannian homogeneous spaces obtained by using some quite natural operations on the first sum \(E\oplus E^*\) of a real space and its dual.