Immersions of real projective spaces into complex projective spaces (Q1111202)

This paper achieves a classification up to regular homotopy of immersions from a real projective space \(P^ n({\mathbb{R}})\) into a complex projective space \(P^ m({\mathbb{C}})\). Calculations with characteristic classes show that, for \(n>m\), any such immersion is nullhomotopic. For \(n\leq m\), both homotopy classes can be realized by immersions, the non-trivial one by the natural embedding. Since \(\pi_ 1\) of the relevant mapping space is trivial, the classification up to regular homotopy of all immersions in a given homotopy class is as for immersions into \({\mathbb{R}}^{2m}\).