Ruh-Vilms Theorems For Minimal Surfaces Without Complex Points and Minimal Lagrangian Surfaces in $\mathbb C P^2$

TL;DR

This paper characterizes minimal surfaces without complex points and minimal Lagrangian surfaces in complex projective plane using Ruh-Vilms type theorems, and explores liftability of immersions into higher-dimensional spheres.

Contribution

It extends Ruh-Vilms theorems to minimal surfaces without complex points and minimal Lagrangian surfaces in  P^2, providing new characterizations and insights.

Findings

Characterization of minimal surfaces without complex points in  P^2

Characterization of minimal Lagrangian surfaces in  P^2

Discussion on liftability of immersions into S^5

Abstract

In this paper we investigate surfaces in $\mathbb C P^2$ without complex points and characterize the minimal surfaces without complex points and the minimal Lagrangian surfaces by Ruh-Vilms type theorems. We also discuss the liftability of an immersion from a surface to $\mathbb C P^2$ into $S^5$ in Appendix A.