Almost complex structures on \(S^{2m}\times\mathbb{C} P^ 2\) and \(S^{2m}\times\mathbb{C} P^ 3\)
\textit{B. Datta} and \textit{S. Subramanian} [Topology Appl. 36, No. 1, 39-42 (1990; Zbl 0711.53030)] showed the nonexistence of almost complex structures on \(S^{2p}\times S^{2q}\) which implies that \(S^{2m} \times\mathbb{C} P^ 1\) has an almost complex structure iff \(m = 0,1,2\) or 3. The main results here state that \(S^{2m}\times\mathbb{C} P^ 2\) has an almost complex structure iff \(m = 0,1\), or 3 and \(S^{2m} \times CP^ 3\) has an almost complex structure iff \(m = 0,1,2,3\).
scientific article; zbMATH DE number 205810