On a notion of nonlocal curvature tensor

TL;DR

This paper introduces a new concept of a nonlocal curvature tensor by extending classical curvature representations and drawing analogies with fractional differential operators, aiming to unify and generalize existing notions.

Contribution

It proposes a novel nonlocal curvature tensor based on generalizing classical curvature and fractional calculus analogies, filling a gap in the mathematical understanding of nonlocal geometric properties.

Findings

Defined a new nonlocal curvature tensor

Established connections with fractional differential operators

Provided a framework for future research in nonlocal geometry

Abstract

In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representation of the classical curvature tensor and by exploiting some analogies with certain fractional differential operators.