The Use of Geometric Quantities in the Tensor Description of a Euclidean Space

TL;DR

This paper introduces a tensor-based framework for Euclidean spaces that highlights geometric vectors and proves integral identities involving vector integrands, enhancing the mathematical tools available for geometric analysis.

Contribution

It presents a novel tensor description emphasizing geometric vectors and demonstrates its effectiveness through proving integral identities.

Findings

Effective tensor framework for Euclidean spaces

Proved several integral identities with vector integrands

Enhanced mathematical tools for geometric analysis

Abstract

We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors. We demonstrate the effectiveness of the approach by proving of a number of integral identities with vector integrands.