# On holomorphic two-spheres with constant curvature in the complex Grassmann manifold G(2,n)

## TL;DR

This paper investigates holomorphic two-spheres with constant curvature in the complex Grassmannian G(2,n), providing explicit characterizations, curvature distributions, and constructing numerous examples of non-homogeneous cases.

## Contribution

It offers a new explicit polynomial characterization of such spheres and constructs many non-homogeneous examples, advancing understanding of their geometric properties.

## Key findings

- Curvature values are explicitly determined.
- Explicit polynomial equations characterize the spheres.
- Many non-homogeneous examples are constructed.

## Abstract

In this paper, the theory of functions of one complex variable is explored to study linearly full unramified holomorphic two-spheres with constant curvature in $G(2,n)$ satisfying that the generated harmonic sequence degenerates at position $2$. Firstly, we determine the value distribution of the curvature and give the explicit characterization of such holomorphic two-spheres in terms of a polynomial equation. Then, applying this characterization, many examples of non-homogeneous constantly curved holomorphic two-spheres are constructed.