We investigate surfaces in the nearly Sasakian -sphere for which the structure vector field is normal to the surface and which are anti-invariant with respect to the nearly Sasakian structure. We show that such surfaces are always minimal. We moreover obtain a correspondence between such surfaces and minimal Lagrangian surfaces in the complex projective space. We also show the same results for surfaces in the nearly cosymplectic -sphere.

Key Words: differential geometry, nearly Sasakian manifold, nearly cosymplectic manifolds, sphere, hypersurface, surface, minimal surface.

2010 Mathematics Subject Classification: Primary 53A10

Secondary 53A40, 53C15, 53D15, 14Q10, 49Q05