Abstract
Pseudo-Riemannian geometry and Hilbert-Schmidt norms are two important fields of research in applied mathematics. One of the main goals of this paper will be to find a link between these two research fields. In this respect, in the present paper, we will introduce and analyze two important quantities in pseudo-Riemannian geometry, namely the H-distorsion and, respectively, the Hessian chi-quotient. This second quantity will be investigated using the Frobenius (Hilbert-Schmidt) norm. Some important examples will be also given, which will prove the validity of the developed theory along the paper.