Some Comments on Projective Quadrics Subordinate to Pseudo-Hermitian Spaces

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 \mathbb R⁺{\mathbb R^{+}} and, further, by taking the quotient (Q)\tilde] = Q￠/U(1){\tilde Q = Q^\prime /U(1)}. The case of signature (1, 1) serves as an illustration. Q̃ is studied as a compactification of \mathbb R ×H_p-1,q-1{\mathbb R \times H_{p-1,q-1}}