Submanifolds of Hermitian symmetric spaces

TL;DR

This paper investigates the properties of submanifolds within Hermitian symmetric spaces, focusing on their geometric relations and answering a specific question posed by Di Scala.

Contribution

It provides new insights into the geometry of submanifolds in Hermitian symmetric spaces, addressing a previously open question.

Findings

Established conditions for non-relativity of submanifolds

Answered Di Scala's question on submanifold relations

Enhanced understanding of Hermitian symmetric space geometry

Abstract

We study the problem of non-relativity for a complex Euclidean space and a bounded symmetric domain equipped with their canonical metrics. In particular, we answer a question raised by Di Scala. This paper is dedicated to the memory of Salah Baouendi, a great teacher and a close friend to many of us.