A formalism for the study of Natural Tensors Fields of type (0,2) on Manifolds and Fibrations

TL;DR

This paper introduces s-spaces to study tensor fields of type (0,2) on manifolds and fibrations, generalizing natural tensors without relying on natural operators or differential invariants.

Contribution

It proposes a new formalism using s-spaces to analyze tensor fields, extending the concept of natural tensors in a novel way.

Findings

Defined s-spaces for tensor analysis

Generalized natural tensor concept without differential invariants

Provided a new framework for tensor fields on manifolds

Abstract

In order to study tensor fields of type (0,2) on manifolds and fibrations we introduce the notion of s-spaces. With the help of these objects we generalized the concept of natural tensor without making use of the theory of natural operators and differential invariants.