On some classes of weakly projective symmetric manifolds

The object of the present paper is to study some classes of weakly projective symmetric manifolds [(WPS).sub.n]. At first some properties of the 1-forms of [(WPS).sub.n] (n > 2) have been studied. Next we consider conformally flat [(WPS).sub.n] (n > 2). Among others we obtain that, in a [(WPS).sub.n] the integral curves of the vector [[rho].sub.3] defined by (1.3), are geodesics under certain condition. Next we consider [(WPS).sub.4] perfect fluid spacetime. Finally, we give an example of a [(WPS).sub.n]. Keywords and Phrases: Weakly symmetric manifolds, Weakly projective symmetric manifolds.
1. Introduction As is well known, symmetric spaces play an important role in differential geometry. The study of Riemannian symmetric spaces was initiated in the late twenties by Cartan [3], [...]