CR-quadrics with a symmetry property

TL;DR

This paper investigates CR-quadrics with a specific symmetry property, providing explicit descriptions of their local automorphisms and presenting numerous examples, inspired by the structure of Shilov boundaries in symmetric domains.

Contribution

It introduces a class of symmetric CR-quadrics and characterizes their local automorphisms explicitly, expanding understanding of their geometric structure.

Findings

Explicit description of non-affine local CR-automorphisms

Construction of a large class of symmetric CR-quadrics

Connection to Shilov boundaries of bounded symmetric domains

Abstract

Motivated by the Shilov boundaries of bounded symmetric domains we consider arbitrary CR-quadrics in a complex linear space (of finite dimension) that have a certain symmetry property. For these the non-affine local CR-automorphisms have a simple explicit description. A large class of examples is presented.