On gap rigidity problems for compact Hermitian symmetric spaces

TL;DR

This paper establishes a gap rigidity theorem for diagonal curves in compact Hermitian symmetric spaces of tube type, extending Mok's noncompact case results, and explores weaker rigidity problems for higher-dimensional submanifolds.

Contribution

It introduces a new gap rigidity theorem for compact Hermitian symmetric spaces of tube type and generalizes the concept to higher-dimensional submanifolds.

Findings

Proved a gap rigidity theorem for diagonal curves in compact Hermitian symmetric spaces of tube type.

Extended the rigidity results to higher-dimensional submanifolds with weaker conditions.

Provided dual analogy to Mok's noncompact case theorem.

Abstract

We prove a gap rigidity theorem for diagonal curves in irreducible compact Hermitian symmetric spaces of tube type, which is a dual analogy to a theorem obtained by Mok in noncompact case. Motivated by the proof we give a theorem on weaker gap rigidity problems for higher dimensional submanifolds.