A New Weyl-like Tensor of Geometric Origin

TL;DR

This paper introduces a hierarchy of new geometric tensors, where each tensor acts as a potential for the next, culminating in a tensor with properties similar to the Weyl tensor, revealing new mathematical and physical insights.

Contribution

The paper presents a novel hierarchy of geometric tensors, including a Weyl-like tensor, with potential applications in understanding geometric and physical phenomena.

Findings

Established a hierarchy of geometric tensors with potential relationships.

Identified a highest-rank tensor sharing properties with the Weyl tensor.

Explored mathematical and physical properties of these tensors.

Abstract

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank-tensor of the hierarchy, possesses all the geometrical properties of the Weyl tensor.