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

TL;DR

This paper constructs explicit non-holomorphic, complete, minimal submanifolds of certain complex and quaternionic projective and hyperbolic spaces using harmonic morphisms, expanding the understanding of minimal submanifold geometry.

Contribution

It introduces new methods to construct minimal submanifolds of codimension two in complex and quaternionic spaces via harmonic morphisms, including non-holomorphic examples.

Findings

Constructed non-holomorphic, complete minimal submanifolds in complex projective and hyperbolic spaces.

Provided complete minimal submanifolds in quaternionic projective and hyperbolic spaces.

All constructed submanifolds are of codimension two.

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.