On the Algebraic Structure of Second Order Symmetric Tensors in 5-Dimensional Space-times

TL;DR

This paper introduces a new algebraic classification method for second order symmetric tensors in 5D space-times, providing Segre types, canonical forms, and foundational theorems on Ricci tensor structure.

Contribution

It presents a novel approach to classify and canonicalize symmetric tensors in 5D space-times, expanding understanding of their algebraic properties.

Findings

Classification of Segre types for symmetric tensors

Canonical forms for each Segre type

Basic algebraic structure theorems for Ricci tensor

Abstract

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is obtained. A theorem which collects together some basic results on the algebraic structure of the Ricci tensor in 5-dimensional space-times is also stated.