Holomorphic isometric embeddings of complex Grassmannians into quadrics: The general case

TL;DR

This paper investigates holomorphic isometric embeddings of complex Grassmannians into quadrics, extending previous results, and explores their moduli spaces using a generalized do Carmo-Wallach theory.

Contribution

It generalizes existing results on embeddings of complex Grassmannians into quadrics and analyzes their moduli spaces through an extended do Carmo-Wallach framework.

Findings

Characterization of moduli spaces of embeddings

Extension of do Carmo-Wallach theory to this context

Identification of conditions for isometric embeddings

Abstract

The present article studies holomorphic isometric embeddings of arbitrary complex Grassmannians into quadrics, generalising results in [13]. The moduli spaces of these embeddings up to gauge and image equivalence are discussed using a generalisation of do Carmo-Wallach theory.