Rigidity of Rank-One Factors of Compact Symmetric Spaces

TL;DR

This paper investigates the geometric properties of rank-one factors in compact symmetric spaces, showing they are uniquely isolated as minimal submanifolds, which enhances understanding of the space's structure.

Contribution

It proves that rank-one factors are isolated as totally geodesic submanifolds, providing new insights into the geometry of compact symmetric spaces.

Findings

Rank-one factors are isolated from inequivalent minimal submanifolds

They are totally geodesic submanifolds

Enhances understanding of symmetric space decomposition

Abstract

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.