Abstract
In this paper, we show that with the nearly Sasakian structure (phi, xi, eta, g) on the 5-dimensional sphere S-5(2) of constant curvature 2 (cf. [21]), there are naturally associated two additional structures (phi(1), xi, eta, g), (phi(2), xi, eta, g) on S-5(2), where S-5(2) (phi(1), xi, eta, g) is homothetic to a Sasakian manifold and S-5(2) (phi(2), xi, eta, g) is a nearly cosymplectic manifold. Similarly, we show that on the unit sphere S-5, which is known to have a nearly cosymplectic structure (phi(1), xi, eta, g) (cf. [2]), there are two additional structures (phi(2), xi, eta, g), (phi(3), xi, eta, g) on S-5 such that S-5 (phi 2, xi, eta, g) is a Sasakian manifold and S-5 (phi(3), xi, eta, g) is a nearly cosymplectic manifold and the last nearly cosymplectic structure is independent of the nearly cosymplectic structure (phi(1), xi, eta, g), in the sense that these three structures satisfy phi(1)phi(2 )= -phi(2)phi(1 )= phi(3), phi(2)phi(3 )= -phi 3 phi(2 )= phi(1) and phi(3)phi(1 )= -phi(1)phi(3 )= phi(2.)