Reducible Conformal Minimal Immersion with Constant Curvature from S^2 to Q_6

TL;DR

This paper investigates conformal minimal immersions of two-spheres into complex hyperquadrics, identifying new examples with constant curvature and analyzing their geometric properties using harmonic map techniques.

Contribution

It characterizes reducible conformal minimal immersions from S^2 to G(2,8;R) and provides explicit examples with identical Gaussian curvature but non-congruent spheres.

Findings

Classified reducible conformal minimal immersions into Q_6.

Constructed examples of non-congruent spheres with same Gaussian curvature.

Analyzed harmonic maps related to minimal immersions.

Abstract

The geometry of conformal minimal two-spheres immersed in G(2,6;R) is studied in this paper by harmonic maps. Then in most cases, we determine the linearly full reducible conformal minimal immersions from S^2 to G(2,8;R) identified with the complex hyperquadric Q_6. We also give some examples, up to an isometry of G(2,8;R), in which none of the spheres are congruent, with the same Gaussian curvature.