Remarks on holomorphic isometric embeddings between bounded symmetric domains

TL;DR

This paper investigates holomorphic isometric embeddings between bounded symmetric domains, demonstrating that such embeddings are totally geodesic when the domains are reducible and share the same rank.

Contribution

It establishes the total geodesy property of holomorphic isometric embeddings between reducible bounded symmetric domains of equal rank.

Findings

Holomorphic isometric embeddings are totally geodesic under specified conditions.

Focus on reducible bounded symmetric domains with the same rank.

Provides theoretical insights into the structure of these embeddings.

Abstract

In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.