Work

Quadratic Forms vs. Metric Tensors: A Foundational Comparison

Year: 2025

Type: article

Abstract: This paper revisits the distinction between quadratic forms and metric tensors. In threedimensional Euclidean geometry, quadratic forms and metrics coincide only in Cartesian coordinates, while in other orthogonal coordinate systems Lamé coefficients must be introduced. By contrast, in Gauss surface geometry quadratic forms alone cannot represent intrinsic curvature; the induced metric is required. We argue that the metric tensor should be interpreted as an invariant property of space, encoding local homogeneity or inhomogeneity and determining curvature.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.17219401

Authors: Rimsha, Viktoras, Rimsha, Laimontas

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7083622642

FWCI:

Cites:

Cited by:

Related to: