Conformal geometry and special holonomy

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.

13 pages. Published in Recent Advances in Geometric Analysis, ALM 11 (2007), pp. 195-209