Conformal geometry and special holonomy

TL;DR

This paper generalizes a classical stability result for minimal submanifolds from complex projective spaces to quaternionic and octonionic cases, offering a unified perspective on conformal and projective geometries.

Contribution

It extends Lawson and Simons' theorem to quaternionic and octonionic projective spaces, providing a broader understanding of minimal submanifold stability.

Findings

Stable minimal submanifolds in quaternionic and octonionic projective spaces are also complex submanifolds.

Unified approach links conformal and projective geometries.

Generalization broadens the scope of minimal submanifold stability results.

Abstract

A theorem of Lawson and Simons states that the only stable minimal submanifolds in complex projective spaces are complex submanifolds. We generalize their result to the cases of quaternionic and octonionic projective spaces. Our approach gives a unified viewpoint towards conformal and projective geometries.