Some comments on projective quadrics subordinate to pseudo--Hermitian spaces

TL;DR

This paper investigates the geometric structure of a specific projective quadric derived from pseudo-Hermitian spaces, focusing on its quotient spaces and their compactifications, with detailed analysis especially in the signature (1,1) case.

Contribution

It provides a detailed analysis of the structure of projective quadrics associated with pseudo-Hermitian spaces and explores their quotient spaces and compactifications.

Findings

Description of the quotient space Q'/U(1) as a compactification of R×H_{p-1,q-1}

Illustration of the case with signature (1,1)

Insights into the geometric properties of projective quadrics in pseudo-Hermitian spaces

Abstract

We study in some detail the structure of the projective quadric Q' obtained by taking the quotient of the isotropic cone in a standard pseudo-Hermitian space H_{p,q} with respect to the positive real numbers R^+ and, further, by taking the quotient Q'/U(1). The case of signature (1,1) serves as an illustration. Q'/U(1) is studied as a compactification of RxH_{p-1,q-1}.