Minimal Submanifolds of The Complex and Quaternionic Projective and Hyperbolic Spaces $\cn P^{2n-1}$, $\hn P^{n-1}$, $\cn H^{2n-1}$, $\hn H^{n-1}$ via Harmonic Morphisms

Abstract

In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic spaces $\cn H^{2n-1}$. We then provide complete minimal submanifolds of the quaternionic projective spaces $\hn P^{n-1}$ and their dual quaternionic hyperbolic spaces $\hn H^{n-1}$. All the constructed minimal submanifolds are of codimension two. Our main tools are complex-valued harmonic morphisms from the above mentioned ambient spaces.