TITLE:
A Vector Tensor Calculus Description of a Euclidean Space
AUTHORS:
Pavel Grinfeld
KEYWORDS:
Tensor Calculus, Differential Geometry, Embedded Surfaces and Curves, Scalar Curvature, Gaussian Curvature
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.3,
March
22,
2023
ABSTRACT: We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.