NOTES ON ORTHOGONAL ALMOST COMPLEX STRUCTURES ON THE RIEMANNIAN PRODUCTS

In this paper, we show that there does not exist an orthogonal almost complex structure on a Riemannian product of a compact Riemann surface with negative constant curvature and a round 4-sphere. In addition, we prove that any orthogonal almost complex structure on a Riemannian product of a compact Riemann surface with negative constant curvature and a round 6-sphere is never integrable.