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
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
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