Classification of conformal minimal immersions from $S^2$ to $G(2,N;\mathbb{C})$ with parallel second fundamental form

TL;DR

This paper classifies all conformal minimal immersions of 2-spheres into complex Grassmannians that have a parallel second fundamental form, providing a complete characterization of such geometric mappings.

Contribution

It provides a complete classification of conformal minimal immersions with parallel second fundamental form from 2-spheres into complex Grassmannians, a problem not fully addressed before.

Findings

All such immersions are explicitly characterized.

The classification covers all possible cases for the given conditions.

Results contribute to the understanding of minimal submanifolds in complex Grassmannians.

Abstract

In this paper, we determine all conformal minimal immersions of 2-spheres in complex Grassmann manifold $G(2,N; \mathbb{C})$ with parallel second fundamental form.